I feel betrayed by my closest friend.
Why do you feel betrayed by him?
Well, he didn't tell me where he was going.
I know it hurts to feel betrayed by someone, but it doesn't seems like your friend did anything particularly bad. Everyone deserves some privacy, and you shouldn't expect your friend to tell you everything they are doing. You will push your friend away if you expect them to tell you every little thing they do.
I'm going to stop talking to him.
I don't think you should stop talking to him altogether, you just need to respect his privacy a little. He doesn't always have to tell you where he's going.