I don't understand why he is giving you the rules for the relationship. I have been married now for a looooong time and fully understand that rules and agreements for the relationship and discussed ad nauseum until there is a consensus. Blanket ultimatums could eventually lead to resentment and anger and an eventual breakdown of the relationship.
As for my opinion: you and your bf don't see eye to eye on an issue that sounds pretty fundamental for you. Your in high school, right? Going off to college? Is this right? If so, there is every chance that this boyfriend will be replaced with bf v2.0 and that bf will adore animals as much as you do.