The main Reason
The movie showed as the main reason for the Captian America Civil war was that government tried to make rules that the humans with superpowers should work according to government orders and they wanted to control Their powers .
And despite of this , the other reason was that winter soldier when he was controlled by the hydra after doing some experiments with him , and then he was used by Hydra and at that time hydra works along with government and hydra controlled humans with super powers and that's why hydra used those person's for their own personal purposes ....
Also hydra by using winter soldier killed parents if iron man and that was the second reason for the fight , and government showed that the bomb blast where t challa's father was giving speech was done by winter soldier was a bait to kill winter soldier as was became out if control to hydra ..