Jealousy is very dangerous because it is essentially envy. Envy is considered one of the seven deadly sins. Jealousy makes people desire something that someone else has. This leads to people trying to take things from other people because they want it. Theft is dangerous to the stability of any place.
Jealousy by itself is not dangerous, it can be a sign of strong love. Most people don't even mind if they see that their spouse or romantic partner is a little jealous - it tells them they are truly loved. But extreme jealousy, as anything else taken to the extreme, is not good, and yes, it can be dangerous. Murders and all kinds of other heinous crimes have been committed out of jealousy.