So everybody has been really hyped about this movie. But do you actually know why this fight is taking place? Why Captain America is against Iron-Man when they were fighting together in Age of Ultron?
Here is the clip that basically explains there point of views
So to trim this down to size, Captain America wants the right to choose. He's really saying that nobody should be in charge of him. He can be his own boss, and he doesn't need the "people with agendas" to tell him what to do, to use him for there gain. He doesn't need to follow them he just wants to do the right thing. I really think it's a matter of trust with Captain America. To sum it up, he's saying that he would rather trust his own judgement rather then something like S.H.I.E.L.D's judgement.
Then we have Tony. He's saying that they don't need the right to choose because it's really not there problem. And even if they don't sign the document that says they give up their rights, it'll be forced upon them anyways, and he's probably right on that.