In the movie Ant-Man, Paul Rudd's Scott Lang seems to lean towards the straight and narrow, after giving up a life of crime. So, why dear reader would he want to buck the system and be on Captain America's side? Let's take a look:
He's a former thief
He's a guy with a record, who did what he did out of altruism, not greed, and got locked up for it. He has a daughter and an ex-wife that he is trying to protect, and with the Registration Act going down in Captain America: Civil War, Lang has no guarantee that his record won't catch up with him or his family if the UN and the powers that be get their way.
He's loyal to Hank Pym
With Hank Pym's low value of Tony Stark and disdain for S.H.I.E.L.D. and other government agencies, it would make sense that Lang would feel the same way. Sticking it to Tony Stark for his mentor would be good motivation.
He's seen what happens when power is abused
From burgling a CEO to help out the common man, to being in prison for stopping Yellow Jacket, Scott Lang has seen what power can do to someone who can't handle it. With the UN and other government entities being able to decide who the Avengers and other heroes can protect or attack, would give the amazing armored master of arthropods reason to help the Star Spangled Avenger.
In case you have forgotten what the stakes are for Civil War, here's a reminder: