Men have heavier pressure put on them by society than women do. Women can have a bad day and people care. They might not really care but they're more likely to adopt the illusion of caring, self-imposed or put on by others, the media, so on, when that woman says "I'm having a really, really bad day."
I'm not suggesting that's the reason more men kill themselves but it's something I've observed, that there could be a gaping, missing portion of the mental health bridge when it comes to men. Both sexes are guilty of it. Men expect other men to be able to hold it together in dire times and women expect men to be emotionally strong. What happens when a man can't handle it or isn't emotionally strong, or breaks? He might become viewed as inferior or weak. If he feels inferior and weak is he likely to reach out for help? No. He's a man. He shouldn't need help. He should be a man and act like one.
I've worked jobs with a large number of staff before and I have seen people say stuff like "hey don't be rude... she's having a rough day" but I've never heard that said about any male employees who openly admitted to being depressed or down. You're having a bad day? Toughen up. Get over it. Oh you're sad? Life is hard. Deal with it.
Men don't get much leeway when it comes to male emotion possibly teetering on the brink of fragility. I personally think, that combined with whatever the fuck they're going through, that pushes a lot of guys over the edge. Why continue on if nobody cares about your general wellbeing?
That's just my theory.