I think you are a little paranoid about your Dad maybe, unless you feel uncomfortable around him for some reason. But, honestly, I have been thinking about this a lot lately. I have a 3 year old son and it never crossed my mind that anything bad would ever happen to him. As soon as my daughter was born it was like I had to protect both of them from the world. I have never been abused or even so much as mistreated by anyone, family or not and I still think about it.
My sister has a 14 year old boy and a 15 year old girl and she has said the same thing. She will allow her son to ride his bike all over town and not think twice about it but, her daughter can't even walk to a friends house 2 blocks over without going in a group of girls.
I think constant exposure to real life news(internet, TV, Facebook...) has made me, and maybe others, hyperaware of what COULD happen and worry that it WILL happen to me or someone I love.