Generalizing a bit here, but, there has to be something mentally unbalanced about a person to randomly, or even intentionally shoot and kill another human being.
This link is so well known and so debated in this country that the end result is that no one can really agree on the definition of mental illness, who should determine mental illness, or even if those who are mentally ill should be restricted from owning a firearm.
SO, it is easier, yes easier for the government to TRY to take away our firearms or restrict everyone in some way than it is to define, diagnose, and enforce restrictions as they pertain to mental illness.
Mental Illness IS the common thread, no doubt in my mind and in my own personal opinion.