After watching Civil War, I was definitely more sympathetic toward Stark and find Cap actually more arrogant in his inability to see things from other's perspective. Fundamentally speaking, I think Stark was trying to save the Avengers from the Avengers. What I mean is this: the one take away lesson from the Age of Ultron is that when the enemy is able to mind control or manipulate and influence an Avenger, catastrophe happens. Ultron may be created by Tony Stark, but it was really Wanda who was the catalyst. Wanda was the one who showed Tony the vision of the end of the world that lead him to create Ultron. Furthermore, it was Wanda again that broke the team down and forced a brawl between Iron Man and the Hulk, with the latter being a city wide mayhem. I believe Stark realized this and realized there needed to be some form of check upon the Avengers. Stark could not believe what Cap believed, that the safest hands are their own. This was because the Sokovia incident had proven that false. The Avengers is composed of some of the smartest, strongest, and most resourceful men on earth. If the Avengers is not in check, another "Sokovia" is bound to happen. Stark feared this, and Stark feared that his mind would be influenced to do something catastrophic again. Therefore, I wouldn't be surprise if Stark feared Wanda, and hence, Wanda was the only person being held in custody during the negotiation (she was able to take down the Vision!).
The theme of mind control or manipulation came up at least thrice more in Civil War. Each time it came up, it created another tear on the fabric of the team's unity. The first one is Bucky, the brain-washed and mind-controlled soldier that was made to assassinate Tony's parents. The second is Cap, his inability to let go of his bond with Bucky (which I argue as Bucky's influence over Cap) allowed Crossbone to initiate his self destruct sequences and tried to understand where Stark is coming from. Finally, Zemo was able to have influence over the Avengers through Tony and Stark, which led to the Avengers splitting. wich was what Tony wanted to prevent all along.
The fundamental flaw of Cap is that he doesn't realize that he is quite literally morally superior than the rest (due to the super soldier serum as explained by Dr. Erskine). He thinks that everyone can be as incorruptible as he is, and that is why he thinks that the safest hands are still his own. Yet, by the end of Civil War, this is no longer true. Cap is not longer morally infallible. Cap is not infallible because he believed in Bucky. Cap is not infallible because he broke his boys out from prison. Cap is infallible because Cap made the (wrong) call not to tell Stark the truth concerning his parent's death. What gave Cap the right to withheld this kind of information? Is that his call to make? That call was not only ethically ambiguous at best, but not telling Stark was also a personal betrayal.