Everyone here is thinking like a product of our culture, which is untterly irrelevant to considering how this father thought and why he reacted the way he did.
Probably the majority of the population in the US support capital punishment and can see absolutely no problem with it. many would see its use extended. Ok, so you do nto think like that, neither do I, but we are not Americans.
Equally many of those who support capital punishment, have right wing views, so far to the right of most of us we cannot see them through binoculars. I can see that a man who is a rightwing political supporter, who supports the use of guns and capital punishment might be so revolted by the knowledge that his son, his won son, has shot and killed, not some fleeing burglar, or other person for whom killing is all they deserve, but one of the icons of his life, the great white hope for the future. He may well be so devastated, so horrified, so revolted by his son's actions, he thinkshe would be better dead.
How you feel how you would react in this situation may be interesting, but predictable, but they are irrelevant. The real iinterest, is what motivates this man's father to do what he did. And his view is as valid as yours.