It is also possible that he has serious self confidence issues he is hiding. Sometimes people try to tear down others because they feel inferior. Either way, I think he at least partially means the jokes.

Does he shows signs of serious self confidence issues in any other way? Has he had a traumatic past? Have you expanded on his claims that you are being combative/tit-for-tat at all? Meaning: have he given you any kind of reasonable explanation as to why he thinks you doing the same thing he is doing is combative/tit-for-tat or do you typically just say you aren't being that way and it gets dropped?