Its true in that "entered into a facility after a suicide attempt" is hand over fist more women and that's where people usually draw from. Because they wouldn't be put into a facility if they succeeded, they'd be dead and going somewhere else.

Its survivorship bias in action. Women who "attempt" and survive will not only appear very visibly, they will almost certainly attempt multiple times. So they are both more bold and double/triple/X-dipping. Men won't even get noticed if they try and since they usually succeed, they only get counted once.