No I'm definitly no expert on this but I'll take a stab at it...I think a father is the symbol of strength and safety no matter what the situation is. Even as you get older, one always looks up to his or her father as a pillar...mothers you can talk to and say what's on your mind...fathers are the one's that "protect the house and the family" a pillar of stregth so to speak..and your fear of someone breaking into the house in a empty apartment might have been your fear of being alone and when you ended up outside and saw your father, that fear went away because you knew that no matter what, he was there to protect you....
(BTW, thanks for the reply to my thread below..I just sent a reply).