>>96405104
As I said, I'm aware horses were smaller pre-1,000 BC; this is shown in art and in skeletal evidence. And, Mongolian horses are also small, but can carry riders just fine. We also have archaeological evidence for horseback riding on the steppe a couple millennia earlier, but not in a combat role.

Breeding for size can have complications, but is pretty straightforward, and animal husbandry was an established practice by the 3rd and 2nd millennium. If it wasn't an issue of temperament, then it might have to do with something anatomical- maybe not size, but a feature of skeletal or connective structure. Carrying a rider could have been hazardous to the horse until some minor anatomical trait was produced, which made riding more viable.