I don't think parents should be looking through your phone, unless perhaps you are quite young and they are checking up on what is going on.
I'm 17 though, and my parents definitely don't look at mine. On the odd occasion my mum will look at my phone when I'm on it, but she knows I don't like that and I'll just put it away. Not like I'm trying to hide anything it's just personal, and I don't look through hers.