The less sexist explanation is that women generally use suicide attempts as a way of asking for help while men generally use suicide attempts as a way of escape.
Stated in those terms, both groups are very competent at achieving the end goal.
Each component of what I stated in response to the comment above is accurate, and an appropriate explanation of the implied assumption in it that suicide lies more commonly with men than women (a common misconception arising from what I explain).
One may disagree with their conclusion that the origin of these problem also has to do with patriarchy, but to claim that these forms of suffering that disproportionately affect men are ignored by feminists is false.
Meanwhile, women have fought long and hard to be accepted as equals in the (voluntary) military.
And you will find many supporters if instead the selective service, you'd support e.g a year of mandatory social service.
You'll also find support to abandon the draft. (it's a highly unnecessary measure in the face of a professional military). You might even find support to have an egalitarian draft if we move further away from a professional military and instead institute mandatory military service.
But "here's a really bad idea that disproportionality affects a specific group, we should double down to affect more groups negatively" just isn't a proposition appealing to many people - male or female.
But this is pretty much the same reason that we don’t see outcry about the lack of women working on garbage trucks: it’s not a desirable thing.
The Google gender pay gap lawsuit was covered extensively a few years ago. It's outcome (men were actually underpaid based on the data) that resulted in a large number of male employees at Google getting payouts and salary boosts was essentially ignored.
It's still unsatisfying at some level though. Reading left-leaning news (say the BBC), you're far more likely to read a story about desirable equality that doesn't mention the undesirable side. To be clear, I'm not opposed to equality at all. The discussion often just doesn't seem to be nuanced.
https://thefeministshop.com/blogs/the-feminist-shop-blog/why...
https://www.washingtonpost.com/outlook/why-the-patriarchy-is...
https://www.tandfonline.com/doi/abs/10.1080/09589236.2018.15...
I'm sure someone with more time (or better yet: deeper familiarity with academic feminist analysis than I have) could find many more.