Since he is the one who broke up with you, and the reason he gave is that he isn’t happy and isn’t sure how to be happy, I think you should move on. This isn’t a break up that has to do with you. It’s about his not being able to be in a relationship right now because he’s in a place in his life where he’s okay. You have to be healthy, yourself, before you can be healthy with someone else. 😉
I agree with you that it’s wrong to try to be friends with an ex. This just makes it way harder to move on, and there’s always that romantic and sexual tension underlying any other relationship dynamic that makes true friendship impossible. So, trust your gut. Be sad that it’s over, but be mature in understanding why and that moving on is what’s best for you.
I hope that helps.