How do you keep your pet from aggro-ing half a raid instance in World of Warcraft

Turn growl off by right-clicking its move in its action bar or in your pet's spell book.

Also take your pet off aggressive. Ideally in instances, it should be on passive with you controlling what the pet is attacking.

Another event that sometimes happens is that you jump off a ledge your pet can't jump off of, and it will run around, aggroing mobs. The easiest thing to do is Dismiss the pet before you jump, and call it back once you landed.