The focus of this verse is strife and quarreling. Some (fools) choose to jump right in and join the fray, while others consciously decide to avoid the conflict.
This proverb states a common theme in the Bible – generally the best response to conflict is to avoid it. Getting involved clouds our good judgment and we can wind up hurting others or getting hurt ourselves!
On the other hand, it is standard operating procedure for a fool to start or perpetuate conflict – even to join someone else’s quarrel. Consequently, a fool finds himself in constant turmoil and continues to perpetuate his own foolishness.
Sadly, he seldom does this in a vacuum – a fool’s involvement in conflict will inevitably bring difficulty into the lives of others, as well. So don’t be a fool, and its best not to hang out with one, either.