Usually a brawl between villains takes place because:
-Their plans interfere with each other.
-They don`t like each other.
-Their close ones are at risk (that is, if they care about them).
-They teamed up, and it didn`t go well.
-The other villain is trying to do harm to the other villain.
There`s other reasons too, of course.
If a villain was a hero at the time, and fought against a villain, it obviously doesn`t count.