Most Helpful Guy
That is seriously sketchy. The fact that he specifically says "I have nothing to hide".
Key here is the fact that you guys aren't on the same page when it comes to trust. Trust, commincation and sex are what i consider the 3 pillars of any relationship. And if you are trusting him with your FB and he isn't with his, something is dis-paired.
Now, i personally, even if i really trusted a girl, would not let her go through my messages, simply because THAT is MY privacy. All relationships need privacy and to give each other space, and perhaps invading it via his messages is something he simply dosent want you going through. He may indeed have nothing to hide but maybe he has a conversation with a buddy regarding you and simply dosent want you miss-interpreting or getting the wrong idea.
But it sounds strange to me that he would specifically say "I have nothing to hide", like he HAS something to hide. Id simply tell my girl "Its my PRIVATE messages, if i show you they won't be private, your invading a little too far". This is also simply due to the fact i haven't been in a long ass term relationship, idealy, if your with someone for a looong time (5+ years) you want to develop enough trust that you can see each other's messages without freaking out, albeit at the same time, if you have that level of trust you shouldent need to see them at all, since you trust each other not to hide anything from each other.
I don't know, its definitely sketchy. If he is asking to see yo shit its because he might not trust you, whereas if he won't let you see his its clearly because he dosent trust you. You got a trust issue you need to sit down with him and talk.