I guarantee you that when/if you get robbed, you will wish you had a gun to kill the sob. You feel violated. I could have shot him but would have been mid torso then head.
No doubt. But if I did kill the sob, I would probably regret it once I cooled down. Feeling angry or violated doesn't justify putting a bag full of possessions over a human life. And it doesn't make it right.
Yes the perp should be brought to justice. Appointing yourself executioner because of petty theft is not justified.