I'll cover up their rhetorical technique with statistics:
Women have outpaced men in Bachelor's degree completions since 1981, and Master's degrees since 1986. At present they are 57.7% of Bachelor's degree recipients and 60.7% of Master's degrees [0]. You might argue that most of the advance women made was prior to the year 2000, so it isn't reflective of trends today.
Women have a "struggle for reproductive rights". Abortion and contraceptives are "critical reproductive healthcare services", according to the White House [1]. Men cannot have abortions, cannot take birth control pills, cannot receive birth control shots or implants, cannot obtain IUDs, and (mostly) cannot choose to have a child without the support of their partner. I suppose, then, men do not even have a chance at having what is a "critical reproductive healthcare service" and are thus inherently deprived.
Women are the heads of four out of five single parent households [2]. Put differently, four out of five men do not obtain custody of their children in situations where the parents do not live together.
Male life expectancy is more than five years less than female life expectancy in the US [3].
The bigger issue than all of this, to me, is the psychological aspect of this discussion that I cannot quantify with large-scale statistics. When men's disadvantages are brought up, society generally shouts "shut up". Since I left my original comment, I have been told that my post was a "hollow unsubstantiated rant", an "incredibly sexist framing", "disingenuous" and "not constructive", "combative" and "alienating". Can you imagine similar attacks being levied against a woman arguing in support of abortion? I sure cannot. Again, I do not know how to quantify this, but the experience of never mentioning an issue which impacts men for fear of being similarly shot down is in the back of my mind every day, and I'd imagine many men face similar thoughts. The thought police hold far more sway over my discourse than I'd like.
[0]: https://nces.ed.gov/programs/digest/d20/tables/dt20_318.10.a...
[1]: https://www.whitehouse.gov/briefing-room/presidential-action...
[2]: https://www.census.gov/content/dam/Census/library/publicatio...
[3]: https://www.cdc.gov/nchs/data/nvsr/nvsr71/nvsr71-01.pdf