If you receive such a communication, you are to take it at face value. It is not open to dispute, whether the comment was offensive. It patently was so, or the matter would not have been brought up. Work it out. We all have hot buttons.
Passionate feeling leads easily to exasperation.
We all can't be walking on eggs all the time, worrying about being offensive. I trod on your foot. And most especially, if someone treads on your foot, you don't turn around and kick them in the shin. You not knowing that, might be unpleasantly surprised to find yourself thus incinerated. Saying nothing about the fact that you feel offended usually leads to a blow-up later on.