May I offer an analogy to this conversation. Imagine you open a door and almost hit somebody in the face. You might think that the person on the other side of the door should have been paying more attention in case somebody opened the door, and of course you didn't intend to or even physically hurt them. In such an instance I would still apologize, because I could have hurt them, and at the very least caused them alarm.
Versatile, I understand where you are coming from not wanting to apologize, feeling you did nothing wrong. And as others have said, that is your right. But in this instance, your words could be misconstrued as suggesting the other poster was not using logic but rather feeling in having this discussion with you. If you had happened to ask me the same question, I would probably have been slightly offended as well, and I am not a woman, because 1) the insinuation that if someone is using feeling then they are not using as much logic and therefore their position is on shaky ground and 2) why would someone's score on Meyers-Briggs even be pertinent to the topic of conversation. So if you really want to continue persuading others to your way of view, I don't feel offending them would be productive toward your goals; if you agree, an apology might be in order, even if the original intent was pure. There is no loss of dignity in apologies or forgiveness.