1. Natasha's whole thing in Civil was to keep the family together and to keep one hand on the Wheel, she needed the Accords as the Accords were at that time the only best option for them to stay together as a team.

2. Steve's whole thing ever since the first Avenger Film is that he doesn't fully trusted the Government. This is what happen when you don't watch the other two Captain America Films that fully told Steve's Story.

3. Wanda was like a Daughter/Baby Sister to Clint, He ain't going to fight her and Natasha, it's either one for another.

Okay here is why the sides are picked

Let's start with Cap's team

Falcon and Bucky makes sense to be on Cap's team because they are close buddies with Steve Rogers

Wanda sided with Cap because he wanted something better for her, plus she probably wouldn't wanted to side with Tony because he created Ultron that got Quicksilver killed and her parents were killed by a Stark Missile

Clint was on Cap's side because I believe he would have gotten along with Steve more over Tony

And as for Scott, well he already knew Falcon which is why Scott was picked for Cap's team. Plus seeing how Hank Pym doesn't like Tony, I don't think Scott would have sided with Tony

Tony's team

Rhodey is best buddies with Tony so he would have sided with Tony no matter what. Plus with him being a part of the military not sure if joining Cap's team would look good to him. Plus he said it was the right thing to do to sign

Vision since he was able to see logic and calculate things out for his choosing to side with Tony

Black Widow has more ties with the government since she revealed a lot of things after The Winter Soldier. So turning her back on the government wouldn't be a good thing

Black Panther probably the main reason is to get revenge on Bucky because he was set up by Zemo who killed his father which he didn't know it until toward the end of the movie. So I don't think Black Panther would have sided with Cap knowing that Bucky is on his team

Spider-Man was just picked because Tony saw potential in Peter being a hero so Peter stayed with Tony

The way I see it, Steve never necessarily fought for the government but fought for American values like civil rights, liberty, pursuit of happiness, etc. If anyone, including the U.S. Government, did anything to go against any of those, he considered them an enemy. Not to mention that he lost in the government after what happened in Winter Soldier where Hydra infiltrated it.

As for Tony, I see it as more like he feels guilty about the Ultron incident but he doesn’t want to feel like the whole situation was his fault so he wants the other Avengers to take accountability as well and he believes that the Accords are the way to do it.

As for the Cap’s team, Sam and Bucky are Steve’s best friends. Not to mention that Bucky is targeted by the government. Clint deeply cares about Wanda and knows how she’ll be affected by the Accords, plus I think he trusts Cap more than the government. Wanda is one of the people that the Accords were meant to target, she’s a powerful superhuman who’s just roaming around in the streets and she took in the Sokovia incident, of course she was going to stand against them. Not to mention, she never like Tony anyway and he was the reason why she joined Hydra in the first place. As for Scott, he’s a fan of Cap and considering his background as a burglar, he’s got to be the most anti-government person on that team.

As for Iron Man’s team, Rhodes is not only Tony’s best friend but also a high ranking government official. Natasha’s whole thing is about winning the trust of the people and that does make sense considering how much she’s done to win the trust of Shield and the government while disbanding from the Red Room. T’Challa mainly wanted to capture the man who he believed murdered his father, who so happened to be on Cap’s team. Plus, Cap stood in his way when he was trying to get to him. As for Peter, Iron Man is his idol so when he came to his apartment asking to fight for him, he did it with no explanation needed. As for Vision, I feel like he believes that him and the Avengers are beings with great power and have great responsibility and he believes that the Accords will make sure that they are held responsible.