Both sides were in the wrong in Civil War.
In concept, Iron Man was in the right. This isn't an issue of pro-government or anti-government, it was an issue of accountability, responsibility, and reward. If a superhero screwed up, then they would be held accountable for their actions, the same way that doctors, policemen, fire fighters, teachers, and other public servants are. It also gave rewards to heroes for their duty. You see, superheroes don't get paid. It's why you often see heroes like Spider-Man have financial trouble. The SHRA paved the way for superheroes and their families to receive pay for their duties, allowing them to be more effective superheroes (you know since they won't have things like a job getting in the way), along with benefits like medical, paid vacation, etc (I dare you to say that someone like Spider-Man doesn't deserve medical insurance). It also provided required training to inexperienced superheroes, if you wanted to be a superhero, you needed to be trained and licensed by the CSA's the Initiative, just like how doctors, lawyers, aviators, plumbers, and other professions are. Without a license, you'd get arrested, and rightfully so. If regular people have to be trained, licensed, and held accounted for, so should superheroes. If regular people can be fined and arrested for not being properly suited for a profession, so should superheroes.
Iron Man also worked very hard to ensure that the government would not outlaw all superheroes and retrofit Sentinels to take down all metas, not just mutants.
Where Iron Man's argument completely fell apart was where he started imprisoning his friends in the Negative Zone without any rights. Cloning Thor wasn't a good idea either. And of course, how he pressured Spider-Man to reveal his identity and unmask on national television (something that even Iron Man admitted was a tactical mistake and was wrong in general) But everywhere else he was in the right.
Captain America was just wrong. Wrong. Wrong. Wrong.