so many more men than women kill themselves.

This can be misleading. More women than men attempt suicide, but male deaths outstrip female due to method lethality - men are more likely to go out with a gun, women more likely to sign out with twin bottles of vodka and vikoden. This could be because more men Really Do Want To Kill Themselves For Real, as opposed to a cry for help, or it could just be that men are far more likely to own a gun and women more likely to have a painkiller addiction.

What is true is that, if diagnosed rates of depression are accurate, a depressed man is more likely to commit suicide than a depressed woman, because more women than men are diagnosed with depression. This might be due to differential rates of hormone production (I wouldn't be able to tell you what, and since any social factors leading to depression are going to end up using hormonal mechanisms as well, the cause of it would be difficult to ascertain), but whether or not that's there men are almost certainly underdiagnosed, since they're less likely to seek out help for mood disorders. It's a very thorny question.