Someone breaks into your home and is rifling thru your belongings without making any threat to you. You hear them and go into that room, if the person attempts to run, let them!
Now if that person turns around and has a knife in his hand or a heavy object and raises it to throw it at you that is when defense is legal.
Very few people remain armed inside their own homes, consequently they meet with the thief unarmed having to retreat and to arm themselves. If the thief doesn't follow you then the threat has subsided and you may decide that you cannot go back into the other room and confront the thief or you may hear the thief leaving your home. Call the police instead. If they are outside DON'T SHOOT THEM!
Now to back up, if you armed yourself before you went to investigate the noise and the thief threatens you, most folks will shoot him rather than retreat. Your Dad may have seen enough dead and/or dying people from gunshots in Nam that he didn't want to bring back those memories again. I would imagine that if he was cornered, self defense would come to the top again and he would have to deal with a wounded, dying thief in his home.
I have known a few people who have said they would kill a guy for stealing food from their refrigerator and when they actually had to deal with the situation the man left home with a full stomach and a lunch bag.
Nobody can predict 100% of the time how they would handle a situation because of slight changes they didn't think about before.
Myself, I keep loaded weapons at each end of the house so I can retreat to a position of authority. I am the kind of guy that if I hear a strange noise in the garage, I arm myself then investigate the noise. Reason: I don't want to succumb to an attacker and have my wife undefended. If someone threatens me I will shoot them with the intent of killing them because I don't know if they have accomplices.
I've seen a bunch of dead and dying in my lifetime, some I cried over, some I yelled, Die, you sorry sob, because they shot or killed a friend. My wife would be very shaken to see a dead or dying person in our home, so I would do my best to see that see is kept from the sight. Killing anyone isn't the easiest thing to do, that I'll guarantee.