When you've been long enough in a relationship, it really doesn't matter what emails, texts, or messages you show to each other. There's no secrets anymore, and you most likely know all each other's passwords anyway. So what if he knows that you like that Instagram pic? So what if she knows that you messaged your brother about how much his sports team sucks?
A secretive relationship - one where you're hiding all your internet and phone activity - can be very damaging to the trust that you share. That's why if she is locking her phone with a new password and not letting you touch it at all, not even to quickly google something, then she must have a really good reason. Like there's some very explicit pictures in there of another man.