Usually a brawl between villains takes place because:
- Their plans interfere with each other.
- They don`t like each other. (A clash of egos and ideologies)
- Their close ones are at risk (that is, if they care about them).
- Temporary alliances are formed, but they soon betray each other afterwards.
- The other villain is trying to do harm to the other villain.
- "Nothing personal. It's just business."
There`s other reasons too, of course. For example, if a villain was a hero at the time, and fought against a villain, it obviously doesn`t count.