How do you know that homelessness isn't caused even more by inappropriate adherence to an aggressive and contemporarily-inappropriate masculine ideal, and that suicide isn't caused by social-media-induced FOMA and increased pressures to conform to ideals? Just because two trends increase at the same time doesn't mean that they're related by anything.

Is there even a good study of gender attitudes prior to becoming homeless (in the U.S.--it's probably different in every country because the safety nets are quite different in different countries)?

It's easy to come up with plausible-sounding stories that fit a point of view (easiest with your own, but if you practice being a lawyer or just a storyteller, it's really not so hard). The hard part is coming up with good evidence that your story is a documentary not fiction.