OP, I'm sorry you tried to have a reasoned and honest conversation with your bf, and it ended this badly. It's really disappointing that he couldn't care about your feelings without mocking them, until you burst into tears. You deserve better than this.

You shouldn't be so dismissed and put down when you've put so much care into dealing with what is in truth a truly ridiculous situation.

Out of interest, did you ask him why he lets Yaz come to him to talk about her bf problems, if he can't stand her so much? What did he say to this?

That is a huge inconsistency, and honestly this situation is a huge mess - Yaz seems to want to maintain an entanglement with both men, and your boyfriend is not behaving in a rational manner - if you don't like someone, you seek to spend less time with them.

I don't see any reason why you should spend more of your energy on this - it sounds like you have other very reasonable doubts about his behaviour (uncontrolled temper), and he's already started mocking you... You know you deserve a partnership with a man who can lovingly and respectfully discuss your feelings.