You can do a couple of things. You can offer an alternative to the way he feels his family sees him. You can tell him that he has wonderful qualities and that he doesn’t have to be “perfect” to be loved. Chances are he won’t believe you, but it’s still important that he hear it.
Even more important: Urge him to get into therapy. This is really a family case but he can start with himself. A therapist will help him get to the point that he can feel strong enough to invite his family to join him in some sessions. My guess is that it isn’t that his parents don’t love him. More likely, his parents have a mistaken idea about how to motivate him.
You also said this started with a move to your town. It may be that the parents are having difficultly adjusting and somehow feel that their son needs to be “perfect” as a way for them to be accepted. I don’t have anywhere near enough information to do more than speculate about that.
Tell your boyfriend for me, please, that withdrawing from everyone and repeatedly telling himself that everyone in the family is against him is only going to drive him deeper into depression. He deserves to be happy. He deserves to feel self-confident and capable. A therapist can help him reclaim his self-esteem and can help heal his relationship with his parents.
I wish you both well.