I believe the point is that if the chance of suicide is very small, and the mentally ill are forbidden from owning guns, it would seemingly be at odds with the claim that "over half of all quoted gun deaths" are suicides.
The claim regarding suicide vs homicide is easy to confirm (https://en.wikipedia.org/wiki/Gun_violence_in_the_United_Sta...). It is not possible to predict every suicide, the best we can do is make an approximation using obvious risk factors like hospitalization for mental illness. There are millions of gun owners in the US, so yes the chance of a suicide is small.