It is often cited that the number of casualties in ancient battles happened once one side gained the upper hand and the other turned tail and fled. Then typically the calvary would ride in and decimate the retreating soldiers.
What I don't understand is why the calvary was able to inflict such lopsided casualties. Wouldn't an infantryman be able to severely wound the horses and slow down the calvary's advance?
You're absolutely right. Footsoldiers can put up an excellent fight against cavalry, both in an individual sense and in a formation. But a rout is not a retreat in good order, where soldiers are under the command of their officers and able to form effective units. A rout is when a group of soldiers has totally lost their cohesion and their morale is beyond repair. They aren't thinking rationally, they're in a blind panic, thinking about nothing beyond GTFO of combat immediately. The primary advantage of cavalry over infantry is that the cavalryman is faster and can maneuver very quickly. Cavalry wouldn't be the only ones in an army pursuing the enemy; footsoldiers chased their opponents as well. But cavalry is able to carry on a sustained and longer pursuit over a good distance, ensuring that the enemy doesn't have the chance to come to their senses and reform. In fact, the tendency for cavalry to stay pursuing fleeing opponents could be quite dangerous for the overall army. Horsemen would sometimes win the immediate engagement they were involved in, chase down their fleeing opponents, then get distracted with looting the enemy camp or undefended baggage. This was much to the consternation of their commanders, who might be losing the overall battle due to the total lack of support from their cavalry. This is what happened with the Italian light cavalry during the Battle of Fornovo in 1495, when they ran off to loot the French baggage train instead of attacking the rear of the French infantry the way they were supposed to do. With their rear secure, the French infantry managed to successfully fight off the allied Italian forces and turned what could have been a crushing defeat into something resembling a victory.
One way of looking at it is that a 100% panic isn't always necessary. While very skilled fighter on foot with a polearm might be able to defeat a horseman, if all his friends have fled and it's suddenly him alone vs 20 horsemen then he isn't going to be anything more than a speed bump. If the horsemen surround our hero and spear him in the back then he likely won't even get the satisfaction of taking an enemy down with him. As a result, even for the few troops who have managed to hang onto their wits running suddenly becomes the only viable option.