IMO three things:

1. As said before, you are attempting to win an argument with a woman who is upset with you. You will not win, and this is further strenghthened by item three which will be revealed soon.

2. Your comment was over the top - if in a professional/work environment. Although we don't know the exact context, I can only assume you work with her? If it's merely friends hanging out, then I suppose it isn't so bad and could be considered harmless ribbing on your part.

3. She probably likes you. She seems to have gotten far too upset for such a quick and thoughtless comment you made. She even took it so far as blaming you for offending her and hurting her feelings. She immediately brought her feelings into the conversation. If she didn't like you she would have just kept her mouth shut and quietly went back to the kitchen to fetch sandwhiches and take care of the dishes. I suggest PIIHB.