First time in the dog house
I think nowadays it is a matter of who you are corresponding on the internet. Today, the internet holds many predators. It sounds like your father is worried about this. It isn't a matter of him NOT trusting you but NOT trusting OTHER people! Many people lie about who they are on the internet. How many stories do you hear about someone meeting someone on the internet and meeting only to get killed, kidnapped, or raped??? Your father just wants to make sure this doesn't happen to you.
It is hurtful that he "snooped" but next time just say: Dad, if you want to know something just ask me. I will tell you.
Good luck and Stay safe!!!