It seems to be the logic that if you tell a shooter that his gun is illegal to possess, he will concede defeat, apologize unreservedly for breaking the law, and stop killing people. But you've got to ask, if he's willing to murder people, is making his gun illegal to carry really going to deter him, and clearly it's not.
No, the logic is that if you tell a law-abiding citizen that his gun is illegal, he will turn it in, and in ten years from then, when he really wants to kill his wife, won't have a weapon.
Or his son won't have a weapon to take and shoot the girls who won't date him.
Or his toddler grandson won't have a gun to shoot an other toddler with.
The world is not cleanly separated into criminals and non-criminals.
It is possible that the laws that work in Europe don't work in the US, as every household there already has several guns, and preventing new ones from being bought will only have an impact when the old ones are broken.
However, not letting known criminals buy guns would be a first step in the right direction.