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

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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?