"Punching up" is still punching. While men are on average more privileged than women, being a man also has disadvantages, and many individual men are actually quite vulnerable. "Punching up" at men causes real harm. Please don't make excuses for misandry.
It's not even punching up. For every one woman who commits suicide, four men will follow her to the grave the same way. More women claim to be lonely than men... my hypothesis is that women actually talk about being lonely while men just kill themselves at a certain point.
I don't think it has anything to do with a fear of being considered feminine. Speaking as a man, I think we are just more inclined to talk about things such as ongoing projects, or things that we saw that interest us, such as an MMA fight or a sci-fi movie.
I believe we are simply less inclined to talk about our feelings. Why? Well, first of all it's just burdensome. It's not fun, and more importantly, it's not exactly productive talking about feelings. That is a reoccurring point of contention between men and women, yes? Feeling vs doing. If a lady says that she is thirsty, a man's first response will be to get that woman some water. It would be much less common for a man to forgo finding water, and instead query the lady on her current emotional state.
"My queen, your thirst is mine. Let us suffer together."