contention
A situation where people strongly disagree or compete for something.
Contention is a state of disagreement or competition, especially when people are arguing about who's right or competing for the same prize. When there's contention over who should be class president, students have different strong opinions and debate their choices. When scientists are in contention over a theory, they disagree about what the evidence shows.
The word also describes the act of claiming or asserting something in an argument. When a student makes the contention that recess should be longer, she's putting forward that idea as something to be debated. A lawyer might open a case by stating her central contention: the main point she'll argue throughout the trial.
In sports and competitions, when someone is in contention, they have a real chance of winning. A runner who stays in contention throughout a race remains close enough to possibly win, even if she's not currently in first place.
A contentious issue is one that causes heated disagreement, like a contentious debate over new school rules. Notice how contention involves real stakes: people care enough to argue, compete, or fight for their position. The word suggests more than casual disagreement; it implies that something important is hanging in the balance.