I've found myself on the receiving end of this 'obsessive defense' more than once in the past and had to completely halt a conversation in order to firmly but compassionately ask the person if they thought I was disagreeing with them and then show them how through statements we've both made we were in complete agreement.

The tenor of the conversation changed almost instantly. It's forced me to be hyper specific when approaching certain topics, but that hasn't come without it's own uncomfortable externalities of conversation.