He wants me to get rid of my cat...

My boyfriend is throwing the biggest fit right now. He wants me to get rid of my cat cause he said he’s severely allergic,(we don’t live together)..and I always make sure I don’t touch my cat before I see him. He said that if i don’t get rid of my cat then we can’t hang out and so that’s means we can’t be with each other.(we’ve been together for 4 years) my parents got me my cat in December when we broke up and i thought we would never get back together.What should I do?