I don't know what problem the lobbying-twisted FCC's rules attempts to solve either. I know what problem net neutrality was supposed to solve.
In short, monolithic providers like Verizon double-bill. They bill you for your packets and then they bill the person you're communicating with for your packets too. It's not like the mail where only one side pays. Both sides have to pay or neither gets served. Naturally, the side who pays more gets to define the nature and shape of the service both side get. As the end-user consumer, that isn't you.
There is an exception: Verizon is part of a cartel of about 20 Internet providers who trade traffic without charging each other. If as a Verizon customer you want to talk to someone buying service from elsewhere in the cartel, Verizon will only charge you. This process is called "peering."
Like the rest of the cartel, Verizon engages in "closed" peering. This means that small businesses and anyone Verizon can bully is excluded and must bend to the double-billing. Here's where net neutrality was supposed to act: by requiring "open" peering where Verizon would trade packets with anyone once *one* of their customers had paid them to do so. No more double-billing.