They tried to set this up as an analogy to other first responders, and the principle isn't entirely unreasonable given the setting (even though a law mandating registration on the basis of who and what you are would never stand up to Constitutional scrutiny) but it didn't make any god damn sense in the execution. Yeah, paramedics and cops and stuff are given extensive training and supposed to be held to account, but superheroes don't choose to be what they are by and large.
Most heroes are gonna do the right thing, and most villains are not, by virtue of their nature. A voluntary scheme set up explicitly to train newbies how best to use their powers, how to keep civilians safe, which kept their identities secret even within most of the organization, etc., would have been accepted by just about everyone except Frank Castle. You'd get some rookies who overestimate themselves at first, sure, but if you get a united front of the Big Shots like Cap and Iron Man and Thor to say "Hey the Superhero Training and Support Act is a great idea, we encourage everyone with powers to register, we can all do better things more effectively" would get a lot of those kids on board anyway.
Instead Tony "Der Fuhrer" Stark decides to fight and throw into negative-zone prison everyone who opposes mandatory registration.
e; Yeah I am pretty confident the movies will do it far better than the comics did, but I will never pass up a chance to bitch about Civil War.