I had other thoughts on the quality of the film (it was good, but not at the level of Winter Soldier or Avengers). This isn't about that. (spoilers anyway though).
One thing that has emerged in the aftermath is people seem to have trouble understanding what Captain America/Steve Rogers basis for "rebellion" against the authorities even is. This is much more clearly spelled out in the comic, but the component parts are all present in the film itself. The problem is they aren't very clear; the movie seems very clearly to be hammering upon questions of revenge instead of the geopolitics that underlie the comic that spawned the film in the first place.
So here's what it breaks into.
1) Cap does not trust the agendas of potential oversight. He has good reason not to from the events of Winter Soldier, to be suspicious of other people telling him what they are up to and for what purpose. The comic was written at the height of the Iraq War's unpopularity. The gist both there and to an admittedly less clear but still present extent in the film is that people in charge often demand weapons and violence be pointed at the "wrong" targets, and this still results in the terrible results they are seeking to prevent by enacting rules of oversight (such as collateral damage). It is an important distinction that the agendas of "ordinary" men are going to differ, perhaps wildly, from what may be objectively found to be good or best possible alternatives. The results may not always be terribly different, but if we're looking for "extraordinary" people to set these agendas, it's possible they may do so more capably and with less damage by not attacking the wrong places deliberately. Winter Soldier sets this up pretty strongly as a concern within the series of films.
2) The film portrays the oversight as coming from the UN via a broad international agreement. But anyone familiar with the UN will be aware it is often dysfunctional and will probably prevent many actions for political reasons ("agendas" as Rogers calls them). "Movie UN" is always a really powerful and cohesive group for some reason. I suppose it wouldn't be very amusing in movie terms to see the UN deadlocking on a vote or Russia or China or the US vetoing deployment of the Avengers to go deal with a raging supermonster/supervillain somewhere on the globe. The question of whether they will be sent somewhere they don't want to go (to do something they shouldn't), or won't be allowed to go somewhere they need to, is a viable concern if what they are doing is dealing with potential threats all over the globe which potentially threaten millions of lives. This is also an argument that many neoconservatives make of course. We are seeing that the threats the Avengers deal with are usually "real"; this is not the case of the US or other nation-states and their agendas.
But. It should be pretty clear that the UN/accords governments ignore the input of the superfriends team of Avengers almost immediately (Ross ignores Stark's file of evidence on Bucky) and that they would end up likely being a huge red tape working on shutting them down rather than using them as a superfriends team to do some good.
3) He does not generally trust the methods of others; again, seeing WS, he presents a very strong civil libertarian case against what SHIELD/Hydra are up to. "This isn't freedom, this is fear". And of course, this being a movie, his fears of what is going on turned out to be quite justified. He has a good degree of trust in the abilities of people he works and trains with closely, and that they are just as concerned that they work carefully to save lives/protect people. He does not trust others to get the job done as often and as well, that there won't be more lives lost. Or that they won't turn out to be weapons that can be turned against the innocent deliberately (as in WS). There's an argument to be made that a team of superheroes with considerable abilities and being well-equipped and trained to use those abilities together will be able to limit the possibility of damage far more than anyone else. Or may be the only ones who can stop certain plots from occurring at all (say some enormous alien invasion of NYC, or cleaning up Stark's mess from creating a psychotic AI, or unraveling and stopping nefarious plots by international bad guys bent on world domination, or whatever).
This is not a great argument in real life. But in the context of the Marvel universe, it probably makes more sense not to attach too much red tape to their activities and to give them the tip of the spear/sword/shield and decide how to use it themselves instead of someone else telling them where they can and cannot go. They aren't just a band of superpowered thugs roaming around blowing things up for kicks. They have spies and computer hackers to help them pick the right targets as best as they can.
The counterargument is strengthened by Stark's screw-ups (with his company selling weapons under the table that he had to clean up, and later himself creating Ultron, but also Vision), which is why that makes a compelling argument to him, but not to Cap. The comic also strengthens this argument in that there are bands of lesser superheroes who cause problems because they are not as skilled or admired or otherwise legitimate, and ultimately this causes more collateral damage.
4) One of the major points in the comic, and which may be obscured by the more personal nature of the film, is that one of Cap's key concerns is that he will be sent after people who do not sign on the dotted line to agree to the rules. And most likely sent after them to kill them, because these are potentially very dangerous people that inspire fear (whether deserved or not). Or at best these would be people who would be imprisoned indefinitely. This point does get made, but very subtly. In the film, Cap was about to sign the accord, until Tony brought up that Wanda was still effectively imprisoned until he signed (plus obviously Falcon and himself). This does not go over well, predictably. Wanda later makes a key point that people are going to be afraid of her no matter what she does. It doesn't actually mean much that she signs a piece of paper (or that Cap signs it for her, essentially).
5) I felt the best argument that was made in the political sense was Widow's "we still will have one hand on the wheel and we have to use it earn back their trust". But, because of the plot of the film in hunting down what ultimately ends up being the wrong man, she sees this isn't going to play out in a way they would have control or influence over what they are to be doing either and bails on it.