I always took this to mean that when Luke’s father took to the dark side and became Darth Vader, in effect, he HAD killed Luke’s father. The good guy had turned into a bad guy, so the bad guy “killed” the good guy. The good guy was no more.
So if I take to a life of crime, by doing so, I’m “killing off” the Good ThelmaLou and replacing her with the Bad ThelmaLou (who, of course, will have to get a newer, badder name).
Did I belabor that too much?