In a recent lecture video, my medieval history professor stated that before the introduction of the stirrup in the 8th century AD, that cavalry warriors in Europe, including the ancient Greeks and Romans, did not fight with big charges or actually on the horse at all. Without the stirrup, they would easily be thrown off the horse after landing a blow on someone else from the force of impact. Rather, they used horses to quickly move from place to place, and then dismounted and fought. The introduction of the stirrup allowed for fighting on the horse itself, and that led to the rise of an elite military class of knights.

This picture seems quite surprising to me. How accurate are these claims? Did the introduction of the stirrup transform the way that Europeans fought on horseback? Did Europeans really not fight on the horse itself before the introduction of the stirrup? And did its introduction actually lead to major social changes?