He has it backwards. Our current physics allow for wormholes. They probably don't exist but if they were literally impossible, then we would need to rewrite our current physics.

Wormholes are more than likely impossible because to hold one open for travel, you would need some sort of negative matter/negative energy. That isn't forbidden by physics, but it's unlikely that it exists since we haven't seen any. Without negative energy/matter to hold a wormhole open, even if you could create one, just a single proton or electron would cause the wormhole to become unstable and collapse in on itself, and doing so faster than the proton could travel through.