Travis, the movie’s protagonist, was relieved of active duty, in the Marine Corps, through the method of honorable discharge; apparently, because he is mentally unstable. He lives in New York City, working as a taxi driver. In the movie, this place is all messed up. Everyone wants a big change instantly and it’s impossible to achieve, so people gives up and doesn’t do anything to improve the city. Travis gets tired of this. He goes out to make a difference. He saves a twelve-year-old girl’s life, killing her pimp and chiefs. He makes use of violence to save her, but he doesn’t think of this as a crime. It doesn’t matter if he has to use violence to achieve this purpose. Anyways, this was what the Marine Corps taught him. The Marine Corps teaches the marines, the country’s heroes, to use violence to protect their country. He is acting just as that, as a country protector.
Travis didn’t like the world in which he lived, but he didn’t do anything to change it at the beginning. What made him go out and kill those guys? I believe that even do he was mentally unstable his most strongly motivation was his love disappointment. We can interpret that Scorsese is telling us that love is a necessity and loosing it can make someone’s mind to get unstable or more unstable than it is already as in Travis’s case.