In the midst of a mass of excited horses moving the same direction in a close group most of the horses won't really even see where they are going. Only some of the horses in front and sides will have much idea of what is going on so even if we assume few ancient people could train horses well enough(poor assumption I think) there are likely a few outliers which could be put in those positions. Even now in dog breeding, some dogs are more aggressive than others even when bred for that trait and part of the expense of cavalry is the training which is intense. Not every horse is cut out to be a charger and there is a reason most chargers were stallions.
Now the final assumption is that all charges by ancient cultures were conducted in the same manner. It seems obvious that not everyone fought in the same style so why would cavalry battles be the same either? I think that accounts for much of the conflicting information. At the same time some heavy cavalries appeared to be much better than others- or at least surviving accounts give that credit.
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