This is for a certain unhappy couple I know and love. No identifiers here. Just a few details and a bit of advice.
She: went into his Facebook account, without permission, found something she didn't like, blew up, is ready to finish the relationship.
He: thought she was snooping, set a trap for her, guaranteeing a confrontation, got it.
OK, guys, here's the bottom line: both of you were stupid! Got that? STOOOOOPID!
Can you get over it? I don't mean never be stupid again. Everybody gets stupid at times, especially in the stresses of a relationship, and including the smartest people I know. Even me. Yep, stupid sometimes. So, can you forgive, work out the issues, and go from there, as in, together? Frankly, if you can't forgive stupid, you're neither of you fit to associate with another human being. All your relationships, whether with partner, siblings, parents or children, will be short and miserable.
First issue: Settle those boundaries. Facebook: private or open to your partner? If private, set up different passcodes. If open, mind what you put on it, just like you ought to be minding what others can see. Employers these days ask for those most personal passcodes. What do you want them to see?
Second issue: Trust. Why the need to snoop? Figure it out, talk about it. No, he's not cheating on you: its appearance was just a trap he set. (Were it otherwise, this would be a very different message.) So what's really going on?
There's a lot of good stuff in your relationship. Remember it. Work on it. Keep it. And remember to keep working on it forever. That's what it takes, for all of us.
I'm rooting for you.