There is nothing "content," or satisfying, about being in contention, and that's probably because the word contention means being in a competition that only one side can win.
"And in this corner, the contender" is heard at most boxing matches to describe each of the fighters about to go into contention in the ring. Sometimes, though, a contention can be a battle of words or a struggle between two parties over a single point. The expression "bone of contention" describes a narrow object of disagreement that reaches the level of strife, or contention. For two hungry dogs, though, the bone of contention might be a serious matter.