There is a very nice co worker at my office. Every morning he comes to my desk and we chat for about fifteen minutes about how our kids are doing and whatnot. I really enjoy these morning conversations.
At one point both him and I had to go through some training courses at work, and one of the courses was taught by an Asian (he was the only Asian) guy. Also both my wife and kids are Asian, and my co worker knows that.
So one morning while talking with him, we get approached and asked if we finished a particular course. Since I do not remember all the course names or what they were about (they were just boring corporate nonsense), I asked if it was a course taught by an Asian guy.
At that point my co worker gets visibly upset. He accuses me of being a racist. I try explaining to him that there was no animosity in my words and that there was no other way for me to describe the guy teaching the course (since they were all almost identical due to corporate world not allowing for much variance in men's appearances). I continuously try to explain to him that people shouldn't hide their race and that my wife and kids are Asian and it would make no sense for me to be racist towards Asians. He keeps on calling me a racist, obtuse and a troll to any explanation I give. Then proceeds expecting an apology and tells me that I should never identify people by their race. At his point I get upset too and tell him that what he is saying is trying to control people's speech and that everyone is entitled to free speech.
At that point he gets up, leaves, and ever since that conversation he has avoided me, and hasn't even said hi back to me if he sees me in the hallway.
He is a very nice guy and very pleasant to talk to. I would like to resume our morning conversations, but him avoiding me doesn't give me a chance to talk. How do I fix things between us without having to apologize since I believe what I have done was not wrong.
UPDATE: So I ended up sending an email to mend things over. We met, I apologized indirectly, he said that he was a bit too sensitive about it and overreacted, and apologized too. So we pretty much both indirectly apologized, and now our morning conversations are resumed, although some damage seems to have been done since now they are not quite as open, but I am sure time will fix that too. I followed exactly what Kate Gregory said, and it worked!