I can't remember ever having someone tell me to man up. The only things people have told me was, "You're so skinny. Eat more. Get bigger." lol.
I hadn't ever really thought of "man up" as being offensive. As some others mentioned earlier in the thread, if it was said to me, it would push me harder to do better. In all honesty, I am definitely not the person with the most empathy in the world. More like the complete opposite. I also don't get offended by ANYTHING, and as a result, I find it hard to see how something that doesn't offend me can offend someone else. While I still don't really get it on an emotional level, after reading 99% of this thread, I can see some ways it can be used that would offend those who do not fit the male stereotype. I have never used "man up" but the example mentioned by Nikotinic about using "gay" to say something sucked is something I got into a bad habit of using frequently. I see how it can be just as demeaning to tell someone to "man up", especially to women, even if not being said to them since it does imply that anything other than man (most people will only think "not man" = woman) is on a lower level.
At the same time though, I do think that it will take a long time for sexism like this to disappear. While it is important for people to start somewhere in going against saying things like "that's so gay" or "man up", I still think in the mean time, people are going to have to live with it. Through reading this thread I also think some people got a bit "too" offended. The reality is, people will continue to say "man up". Some will use it in a good way, others will use it in a demeaning way, but you're going to have to deal with it.
In my opinion, anyone telling someone to "man up" in a demeaning way probably has some issues of their own (as in insecurities) just like how so much homophobes turn out to be gay themselves. If someone says this to another person in a demeaning way, showing you don't care will show that you are sure enough of yourself not to give a rat's ass about their opinion on such a thing, and honestly, they probably won't say it to you again. If everyone did this, imagine? I never really had much of the woman's experience, so I can't really comment on that other than saying being successful in your career or whatever you want to do is the best way to show the world a woman can do anything.
tl;dr People are dumb.