Other forms: contentiously
A contentious issue is one that people are likely to argue about, and a contentious person is someone who likes to argue or fight.
Some issues are very controversial. They're also contentious, because people tend to argue about them, and the arguments will probably go on forever. Contentious issues get people angry and in a fighting mood. On the other hand, some people always seem to be in a fighting mood, no matter what the issue is. People like that are contentious too.