Man, you're hunting for sexism where there is none.

The original comment was two sentences long. And contained no argument to speak of. Just a poorly thought out, knee-jerk reaction that she would (rightly) immediately reject if the sexes were reversed. So I responded to it with the sarcasm it deserved. It wasn't a strawman at all, I did address what she said. It's just that what she said was so silly there wasn't much to work with.

Your comment contained an actual argument, albeit also a silly one, and while I responded to it with slightly less sarcasm, there's a reasonable case to be made that I responded to your argument less respectfully than I did hers. Because she didn't detect the sarcasm in my reply, she responded with a simple "thank you," thinking that I'd agreed with her. There was no room for you to make the same mistake.

And this, fundamentally is the point. It is asinine to say that because my response to a woman was different to my response to a man, this must be evidence of sexism. Because you haven't taken into account the content of the messages. One hundred different men could have written comments and my reponse to each of them would have been different. And the difference in those responses would be evidence of nothing except the differences in the ways those men constructed their arguments. This is true for the original author too.