Because gun ownership itself is a mental illness, born of paranoia and inadequacies.
I wouldn't go as far as to say that gun ownership is intrinsically "a mental illness". The paranoid, the insecure, and the hateful are absolutely attracted by the notion of gun ownership for harmful reasons. However, I think there are some legitimate reasons for the ownership of old-fashioned guns as well: home defense, hunting of invasive species, skeet shooting. I don't think these reasons outweigh the public's right to life, but I am willing to compromise.
I see no reason to allow concealable weapons or modern assault rifles and weapons similarly able to inflict mass carnage efficiently to be possessed by civilians, but I also don't think any attempt to ban them will be successful.
A heavily restricted ownership process consisting of psychological and medical testing, a comprehensive background check, and a mandatory national database of gun owners cross referenced with up-to-date medical and psychological records is necessary. I also think that a ban on the possession of unregistered weapons (so they can be confiscated) and a proliferation of smart gun technology should be pushed too.