The issue is the “man” up aspect. There are ABSOLUTELY times when you have to… Well, man up, nut up… Whatever. That’s a fact of life - some situations require you to stop being a child, and instead face it like an adult would.
We run into issues with it being ‘man’ or ‘nut’ - these are gender-loaded terms, which imply that females aren’t able to do the same thing. Do I think anyone actually means that when they say one of those things? No. Do I think a lot of reactions to them are overblown? Yes. We should still be cognizant of what the language we choose to use may say subtextually though.
There’s another parallel issue to the advice to man up. That’s that a lot of times, the people who get that advice HAVE BEEN manning up, and the advice giver is seeing them in a moment where they’ve been worn down and just need a quick whinge fest before going back to manning it up. Situations like that imply that having any emotions other than “git er dun” is a bad thing and you should just STFU and work.
As far as giving others advice goes, generally speaking unless they ask you for advice, don’t. If someone’s just coming to you with some venting about a thing and you tell them whatever version of “man up” you want, even if it’s applicable, it comes across as dismissive. The person may not want advice, they may just want to unload a bit. If you can’t do that without offering advice, then it’s best to state that.