When it comes to self harm, I think BPD. There's a big difference between the sexes there too. Boys get abandoned, abused, neglected, molested, etc. But the dysfunctional behavior turns out differently. Going out and instigating physical fights/insane risk taking as a way to reassure themselves they can take care of themselves. Whereas (from the outside) it looks like women with BPD have a stronger drive to make sure other people will be there for them.
Traits we associate with masculinity/manhood have powerful, shared internal drivers. Being really sick prevents you from doing the things that men derive wellness from. Being useless is psychologically devastating for men (look at the suicide/addiction rates post disability). Not being strong/providing means that you can't protect your family/friends. That's deeply distressing to most men.
The men I know who malinger/I suspect of light munching all have some pretty crippling mental health issues that keep them from fulfilling their masculine obligations (contribute/protect/provide), or desires (love, fatherhood, respect). The men who have physical issues might overplay them, because they don't feel they justify the degree to which they can't do those things. Women have a need for those things too, just with a different priority and way.
We see that with some of the girls who turn to hardcore munching after failure to launch. It just seems to be a matter of degrees. Why women appear to take it further, IDK. I psuedoscientifically suspect that the reason has to do with motherhood (both internally and socially) - some women get totally debilitated by dizziness, vomiting, and other stuff the entire time their pregnant. Late pregnancy/labor/birthing are physically disabling, and it looks like it takes a couple of days to recover at minimum. So women might be internally more accepting/less distressed, and more socially supported.