I have a very similar problem but in my case the coworker is my boss. I have basically had to tell him he is wrong and that nothing he is going to say to me is going to change my mind and that I want no more of that conversation, I then change it to something work related. Sadly this has become the new normal. Thankfully my boss is expected to retire in December so I just need to wait it out.
My coworkers tell me that I am the hero of the group for shutting the boss down in such a loud and aggressive way. But its so exhausting.