We live in a sexist world therefore even more sexism is necessary to eradicate the sexism.

Pretty brilliant logic, there. You missed OP's point entirely.

I don't think you read danr's logic correctly, but I could be wrong.

I interpreted it as "The reason women want to be treated differently [from how they are NOW] is that the world is a sexist place." Not, "The reason women want to be treated differently [from MEN] is that the world is a sexist place."

Either you are wrong or danr shifted goalposts, then. lohengramm's point pretty clearly is talking about women being treated differently from men, not women being treated differently from how they are now.

Affirmative action != Sexism

Affirmative action is exactly sexism (or racism when applied to race); it is just claimed to be justified.

Even those who advocate for affirmative action generally do not deny this. You are behind the times.

If finding that we live in a sexist world is a good reason to be even more sexist, then you can throw away every movement that tries to do the opposite.

"some guys don't know how to act around women", it was said. Well, people should know how to act around people, no matter gender or race. This statement does not collaborate to end with any kind of discrimination: it is already discriminating.

You need to realize that what you perceive to be sexism for the benefit of women is actually affirmative action because of the discrimination they suffer from.