Most Helpful Guy
To draw "he's cheating" out of that isn't good. That shows me you don't trust him. Whether that's you having a problem trusting people, or him being suspicious, or both, I can't say I have enough info to really tell. Not posting a picture of you on his FB isn't something I'd personally label as suspicious, if you want my input on that.
No one here (or anywhere for that matter) can give you more of an accurate answer as to why he doesn't do that than him, so the answer there is to ask him.