My boyfriend keeps threatening to break up with me?

It has happened multiple times where we fight he makes comments at the end of each fight. For example, I had suggested that we take some space for 2 or 3 days to cool off the hurt, but he says "Ill try and remember to message you, if I dont forget about you". He has also said things like "I dont want to talk to you anymore, good luck" or "If I dont talk to you in 2 or 3 days it means I disappeared and Im done" and "Since you said that feeling guilty about breaking up with you feels less".

He says these things when I say whats on my mind and try to recorrect him on a misunderstanding or what I consider inappropriate behaviour (e. g., belittling me in a fight and not respectful). I apologise for what I said and he comes right back.

My family and friends notice I cry a lot due to these occurrences. I cry twice a month. Is this even normal to be doing this?
Updates
9 mo
Hi, thanks for everyone's responses. I have spoken to him about his behaviour, how it is deeply hurtful and it is not right for him to do those things. He also realises it, and he knows now it does hurt me a lot and he shouldn't be like that towards me. He is going to work on his behaviour and keep himself in check. I told him if he doesn't, I will. If he gets worse Im out. Thanks!
My boyfriend keeps threatening to break up with me?
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