I've only seen the movies, never read the books, but I think at first he wanted to, as a big blood purist sort of character but then when Voldy actually came back Draco became scared of him and what he had become and had become a death eater to protect himself and his family.
In book 2 of Harry Potter he said "even if Harry was the heir of slyterin i would've helped him stupify all of those Mudbloods" (i read it in NL and i don't remember EVERYTHING he said cause i got that book from the library so i don't remember everything he said) so he was basicly wanted/bragging to be a death eater but then when he became a death eater he realised how bad it was and didn't want to become one anymore
@Masqueradess If he wanted it, at least in my opinion, then it's not being forced. However, to be fair, I think he was forced to stay a death eater, because he clearly did want to leave at some point, even if he wasn't forced into becoming one.