Isn't the whole point of a gun to kill people though, unlike a car?
Is that an indictment against cars? The whole of your life depends upon the good will of others.
The baseline is that, as the Constitution enumerates, armament of self for defense of self, family, and state is a natural right. The well-established & well-understood caveat is that any right may be curtailed for a particular individual IF adjudicated, in court, for good and established specific cause.
The problem being addressed by the law in question is that veterans are being denied that right by faceless bureaucrats routinely checking "mentally incapacitated" checkbox for decades-old never-recurring cases of mild depression or other irrelevant trivialities. If you're going to deny someone the right of self-defense, at least do it in court with articulable & relevant cause.
It may seem a subtle difference, but it's important. Another way I've heard this said: "My pistol serves not to impose my will upon others through force but to ensure that others may not do so unopposed."