Called a Liar

Just trying to understand why my bf gets upset. He thinks I logged into his facebook and actually I haven't been on his facebook since he changed his password and I have no clue what it could even be. So my question is how do I get him to believe me even after I told him he can go thru my phone and look cause I honestly have nothing to hide from him. But he hides chatheads when they come in so I don't see who he's talking to and I tell him exactly who I talk to. Ugh not sure what to do. Needing some pick me ups.