Would it be OK if I opened my housemate's mail?
Why would you do something so nosy?
I'm so tempted to do it because I think he's hiding something from me.
You'd be doing something illegal though! You can't just go around opening people's mail without their permission. It'd land you in legal trouble if you get caught.
But I have to know what he's hiding from me. He doesn't trust me.
He doesn't trust you because you're the type to snoop on him. If you want to gain his trust, you need to stop trying to snoop on his mail.