I've seen a number of posts that paint transgenderism in the same vein as plastic surgeries and other such modifications to self born out of insecurity and dislike of one's appearance. This is a very fundamental misunderstanding of the transgender condition.
You're conflating dissonance with dissatisfaction. They can go hand-in-hand, but you need to realize that they are still two very discrete concepts.

To put it more plainly, body dysmorphia (dissatisfaction with one's appearance) and gender dysphoria (dissonance with the gendered aspects of one's body and social perception) are not the same. The former being so common in our society makes it easy to assume the latter is inexorably tied to it: virtually everyone in our society considers some parts of their bodies flawed or undesirable, and trans people are no exception; in fact, their gender dysphoria is often exponentially amplified by this, especially with trans women, who (if entering gender transition to female after puberty) have the misfortune of nearly irreversible virilization (facial hair, masculine features, etc), which is considered almost universally "unattractive" as far as social expectations for women go. So, it is no surprise that insecurity would result. Our culture is fairly vicious about standards of beauty for females as indicative of their worth to others-- how many overweight, 'plain-looking' women do you see represented as successful (or even just respectable) in television or movies, verses overweight, plain-looking men? Or perhaps just think about the rate of eating disorders among women, many of whom are fairly conventionally attractive to begin with (though not to themselves, given judgmental cultural pressures).

As for my background: I am a transsexual man (meaning I was perceived as-- or was, depending on your choice of definition-- female during my childhood); I won't hide that bias.
While I won't claim to be an all-out leading expert on transgenderism, I've worked closely with some that are, due to having worked on research about the topic during my studies at Yale. My experience with it is fairly extensive, both in an academic (and yes, having studied oppositional and supportive sides) and personal way.

To get back to addressing the point that was being asserted, I'll relate my experience with the difference between these similar concepts.

To be dissonant with the gendered aspects of oneself, as stated previously, does not necessarily mean that one is dissatisfied with one's appearance, or that change is sought for the sake of improving that. For example, in myself, while I certainly experienced insecurity with my appearance when I was younger, this was not at all true by the time I finally came to terms with and acknowledged the gender issues I had continually pushed down out of fear; in fact, having resolved those insecurities had been, in my mind, a prerequisite to even allowing myself to humor the possibility of gendered distress having been anything more than a misinterpreted symptom of a different insecurity (from a misogynistic culture? from a culture critical of appearance? something else?). In fact, I wanted desperately for it to have been one of those things-- I spent countless months of soul-searching and written self-analysis on each possibility hoping to uncover that it was, in fact, just some kind of misplaced dissatisfaction with my body on some aspect of attractiveness, or just some kind of bitterness with mistreatment of women in society, even some consequence of some sort of abuse (that I can't recall, given that I have not actually experienced that), etc, etc. I wanted that, because it would have been so much simpler, easier, more understandable. To have a deep and intractable dissonance with the sex and gendered characteristics of one's body is terrifying, largely because there is no way to address it-- or even really acknowledge it-- that is even remotely socially acceptable. Even without any relation to sexuality (having existed since my earliest memories as a toddler, as described in many others), it is considered perverse, deviant, a pitiful and somewhat disgusting manifestation of a twisted mental illness. And yet, by all other accounts, I am and was sane, even considered a straight-laced and respectable 'goody-two-shoes' to many-- and to acknowledge this condition is to realize that latter perception by others will be traded, both in the minds of many already known and quite especially in the minds of strangers, for the former. Knowing that those feelings are not going away-- again, having persisted from earliest childhood-- and yet knowing that expressing them for the sake of one's happiness is to virtually guarantee a future of discrimination (legally, socially, medically), rejection (both by those who already know you and especially those who don't), and to essentially be cast to the lowest class of our social order in almost every sense-- it's terrifying. It's overwhelming, very much to the point of hopelessness and despondency. That's essentially the source of the high depression and suicide rates amount transgender youth, as well as the reason so many just continue to repress it for so long, hoping desperately that it will just go away on its own as adulthood progresses (and it doesn't, which is the source of those who transition later in life).

And again, back to what I was saying: I did not consider my body unappealing, in terms of attractiveness, in the least. I was able to recognize, in fact, that it was quite beautiful-- my appreciation for myself, physically and mentally, developed quite slowly, as it was (and still is) completely heartfelt and sincere-- a journey that takes considerable time. But I earnestly loved my arms, my legs, my stomach, my face, my hair, and I also saw my breasts, nether regions, hips, and general femininity as beautiful: but there is a difference between seeing something as beautiful-- valuable-- even desirable (to some), and to lack dissonance with it as an aspect of one's body and being. A straight man can look at a woman and find her unfathomably beautiful without having the least desire to be in her body-- in fact, it would likely horrify him if he were suddenly forced to spend the rest of his life wearing her dresses, being expected to behave in the same feminine way, and otherwise socially regarded as a woman (even if others considered him attractive in that role!). The problem largely lies in that there is no way to really put in words this dissonance with one's physical sex. "Trapped in the body of...” is a phrase many resort to, largely for the benefit of the cisgender audience's understanding (and there are certainly trans folks who find it close enough of an approximation to identify with it), but it is not really what gender dysphoria is. Again, it's not something that can be put in words-- much like numerous other medical conditions or physical states, you cannot truly make a person understand it if they have not experienced it. Try to describe pain to someone who has never felt pain, or marijuana to someone who has never ingested it (I haven't, so go ahead). You can try to approximate it, but you can't truly convey it in the most integral level. Gender dissonance is just that: a strange and indescribable-- yet despairingly inexorable-- feeling of disconnection with exactly just the gendered parts of one's body (and potential the social mores in association)-- not any part else, and not on basis of attractiveness (though certainly body dysmorphia can coexist). Perhaps it could be likened to the 'phantom limb' phenomenon. There is the feeling that while this body part is part of you, it somehow, in some strange way, does not belong-- it feels wrong, "off", somehow, not quite right, but it's not something that can really be put into words. It's not a delusion that the body part is not physically yours, and it's not a delusional belief that you "are" something you physically aren't. Rather, it is full awareness of the state of one's body, concurrent with an indescribable dissonance regarding the primary and secondary sexual characteristics resultant from how one's gonads differentiated in the womb-- followed by the realization, after fully analyzing one's deepest feelings, and every potential alternative solution, that the only real way to address and alleviate this discomfort is medical intervention via gender transition. The purpose of medical science is to improve quality of life and decrease morbidity for those with conditions that negatively influence those values, even for those whose conditions and treatment challenge our preconceived notions about the determinate 'source' of gender (to most, genitals). Transgenderism has existed for centuries, throughout every culture and region of the world, and efforts to 'cure' it have never ceased. Despite this, no attempt to reverse the condition has ever met real success, and the only action which has consistently shown to improve the quality of life and outcome for these patients-- and statistically, it does so in quite a dramatic way-- has been to "humor" the transgender condition and allow these people to live life as they desire.

Of course, when it comes down to it, the very nature of its indescribability is what leaves it open to criticism and derision from others: people tend not to believe what they cannot experience for themselves and which falls so far outside of comparability with what they have.
Moreover, it’s virtually impossible to truly prove that the root of the phenomenon is strictly physical or mental in nature. Part of the problem there lies in that those aspects of our being are less distinct and separable than the public tends to treat them-- after all, it wouldn't be possible to treat mental illness with medication otherwise, and we can see fairly well through history how mental (or physical) medical conditions being regarded as just some deficiency in willpower or defect in character has generally worked out-- but even so, that latter perception remains in our society for virtually all forms of mental illness, even those we have actually proven as inseparable from the physical (chemical) state of the body.

The reality is that the evidence in research of transgenderism, in terms of having proved it as an irreversible and permanent state of being, is virtually identical to the same in the field of homosexuality. And, in fact, if you look at how these things are generally argued-- you'll find that the exact arguments previously used to discredit homosexuality are the ones that continue to be used against transgenderism: 'It's insecurity, it's delusion, it's sexual deviance, it was childhood abuse, it is just mental illness to be fixed,' etc, etc. The only difference is that the public perception of homosexuality has shifted, in large part due to media exposure, such that LGB folks are recognized in their sanity and otherwise 'normalness' aside from their (harmless) sexual preference. Yet the same is not true for transgender people, no matter how many of us are demonstrably sane, intelligent, kind, capable people, and regardless of how the condition (and its treatment) affects no one but its own sufferer.

In the end, given that it is impossible to prove one way or the other-- in the same vein it is impossible in the field of homosexuality as well-- that it is a condition based in physical development, or that of the mind, with the usual connotation of being 'acceptable' or 'unacceptable' respectively, due to our cultural ideas about willpower as the real cure to mental conditions... It is only up to you, according to your own conscience and desire or lack thereof to dictate others' lives, to decide how you will choose to regard transgender people. You can choose kindness, to respect others, to give them the benefit of the doubt when they express how they feel, and to choose to believe them when they say that transition improved their quality of life-- because what harm will it really cause you to believe, versus not to believe, in opposition to what incredible harm you can and will cause by rejecting them?-- or you can choose incredulity, choose to disbelieve them, to reject their identities and well-being, and to hoist upon them how you believe they should feel and how you believe they should live their lives, lambasting any efforts by others in legal, social, technological, or other sectors to accommodate what you think should not even be allowed to exist... No matter how many centuries it has.

Yes, of course my bias shows in the tone of how I write. Quite pointedly. But it is easy to be biased when the widespread consequence of your individual choice to discard empathy-- 'corrective' camps and counseling, a 1 in 12 murder rate, endemic poverty due to difficulty gaining employment because of social prejudice and lack of laws in most areas (which are continually shot down when proposed) protecting against blatant firing for transgenderism alone, a 20-50% suicide attempt rate, never-ending harassment, hell, even sometimes the inability to use the correct damn restroom without breaking the law in the process-- is so disproportionate against the consequence, for you, to choose being tolerant-- what? Discomfort, disapproval, maybe disgust, in imagining us living lives without discrimination and rejection at every turn? What harm does it really cause you? Do you think you should be the arbiter of evaluating our worthiness and sanity, regardless of what research and statistics show about our well-being? Do you perhaps consider us a menace to society somehow, from the trans female Professor of Forestry at Yale, to the trans male Professor of Neurology at Stanford, to such past figures as Alan L. Hart, the trans man who pioneered x-ray technology in diagnosis of tuberculosis, saving thousands of lives?
Why do you think you better understand the inner workings of a condition than those who lived with it their entire lifespan, and yet still conducted themselves with intelligence, strength, and quality of character equal or better to many 'sane' or 'normal' people? That you are a better judge of what should be done with it, even, than the research that has consistently shown gender transition to yield the most favorable outcomes?
Who are you to decide what harmless definitions of happiness in life others are allowed to pursue?