Here's the thing about mental illness and guns. People's mental health changes. So you may be a completely mentally stable individual when you buy the gun, but because the U.S. requires no continuing checks for gun owners, there is absolutely no oversight regarding people whose mental health status changes.
1 in 4 adults experience some form of serious mental illness in a given year. Many people will experience some form of mental illness over their lifetime, with major depression being the most common.
Mentally ill isn't necessarily something you are or you aren't; for many people it is a transitory condition. For others, it's chronic. But even when discussing the forms of chronic mental illness, many of them don't appear until people are in their thirties. It's a common time for mood disorders and schizophrenia to crop up, in men in particular, because their brains have on finally stopped changing.
So the responsible gun owner at twenty-five might be the guy who thinks meter maids are controlling his mind, and go on a shooting spree. As long as there's a feeble, one-time check to see if you've been forcibly committed, and no follow up, we'll never successfully deal with the juncture of mental illness and firearms that have caused so much tragedy.
Finally, as always, remember that the vast majority of mentally ill people will never commit an act of violence, that most violent crimes are due to factors other than mental illness, and that the person most endangered by a mentally ill person having a gun is themselves.