It's not hard to understand. Three things have been happening all at the same time in Europe, and each one of these are, all by itself, of the kind that prompts governments to go into authoritarian mode. All three put together make this exponentially more the case:
a) Risk of Russian invasion.
Russia has already been attacking NATO countries via invasion of their airspace via drone fleets and military aircraft, plus several cases of cutting oceanic data cables, and other forms of harassment, including explicit verbal threats against several members.
Preparing for war requires managing citizens morale. Completely free flow of information is detrimental to this effect, since either true of false (propaganda) content telling citizens the war is going bad can become a self-fulling prophecy. Hence, governments see the need to start implementing all the technology needed for effective control of information flow right before and during a war if it happens.
b) Rise of internal threats.
First and foremost, the far-right parties on those countries have been growing in popularity and power, being financed as a 5th column by Russia. If victorious, they will fracture the EU, weakening them all against aggressors. Additionally, European leaders fear losing power and, in the extreme, losing their lives and freedom to far-right extremists.
As such the see the curbing of those propaganda efforts as absolutely necessary for the survival of their, well, everything.
b) Betrayal by a former major ally.
The US has sided with the enemy of Europe, Russia, on a number of fronts, having been undermining the European effort in the buffer zone between Europe and Russia (aka Ukraine), helping to fund the above internal threats, relentlessly pressuring European countries on all economic fronts, and actively threatening to invade and conquer European territories, meaning what was a risk of a war on a single front has grown into a serious risk of a two-fronts war. Additionally, the US controls most of the information exchange technology Europe uses, meaning it can advance the propaganda mentioned above way more effectively than Russia alone could, and get intelligence on Europe at levels Russia alone absolutely wouldn't be able to.
As such, transferring control of information channels from US national security associates to European ones became urgent, with an immediate need to reduce as much as possible the power the US has to advance those contrary goals, which again requires controlling information flows.
Hence the recent push.
Notice I don't agree with any of the above. I'm of the "the best counter to bad speech is more speech" school of thought myself. But that's what I see as the core motivations behind this movement.
As for the US, it's trying to implement a Fascist political regime. As any such movement, it uses the tools of freedom to raise, then once in power destroys those tools. As such, what we're observing over there is much simpler than what's going on Europe, even if the end result, if it arrives at its goal, is pretty much the same.
And other countries are following so many variations of the same issues.
