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 — like abortion, the death penalty, and gun control — 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.

Definitions of contentious

adj inclined or showing an inclination to dispute or disagree, even to engage in law suits

“a style described as abrasive and contentious
combative, disputatious, disputative, litigious
given to or characterized by argument

adj involving or likely to cause controversy

“"a central and contentious element of the book"- Tim W.Ferfuson”
marked by or capable of arousing controversy