Cheating??

So just the other day my boyfriend and I were Snapchatting about wether we found it okay to get on each others phones or not. He told me I could have his phone password and get on his whenever I wanted, he can get on mine. Then I asked him if I'd be allowed to have his password to things like fb and snapchat. He basically told me that I could absolutely not have them and there was no reason for me to have them. The thing is, he has a history of cheating. He cheated on his ex (baby momma) from what I've been told. He told me that the reason I couldn't have them is because his ex would get mad at past relationships. I think its so shady that he'll let me get on his phone and not his social media, like he could easily delete things before I come around. What do you guys think. Also, he always accuses me of cheating when I go out with my guy friends (who are gay). Or just whenever. Does this sound like the actions of a cheater!