I dunno, I get why some find it offensive but personally I get a boost when my coach uses it between sparring rounds or when I'm hurt, I'm fading or I'm close to the finish looking for that last push. For me it's more of a motivational booster, something that pushes me past my limit. The way we've discussed it in class is more that in our minds it's SuperhuMAN up. There's little short motivational boosts. "You got this" seems so passive. Like what you're doing is enough and you don't need to push youself. But "man up" feels like you have to physically power up to that extra level.
Yeah it's maybe not the best idea but for us at Taekwon-do, it works. Boy and girl alike. But I think it's one of those things where sometimes people like it and sometimes they don't, and if they don't you don't use it with them. I see it the same way I see swearing. Some love it and some hate it. Where one group find it offensive and wrong, the other find it adds to the strength of language and isn't evil. Neither group is essentially right or wrong. We could debate all day on this one and never have a conclusion.
I do think that "man up" and "be a man" shouldn't be used around kids IMO. I think it to be harmful on an emotional level when used attached to overly stereotypically masculine ways. However, at the same time, is saying that a boy who knocks up a girl should "be a man" and be there for mother and child a bad association? Maybe if these phrases were attached more to positive affirmation in less stereotypical masculine fueled ways we'd see it in a different light.