If you say something that is intended to make people angry with each other, your words are divisive. For example, saying "only stupid people like dogs" are words divisive enough to get people fighting mad — at you!
The adjective divisive is related to the verb divide, which means "to separate things or pull them apart." Divisive things divide. That's why it's best to avoid potentially divisive topics like politics if you believe you are in the company of people who have differing opinions. Don't confuse divisive with decisive, which means "able to make decisions" and "unmistakable, beyond a doubt."