Imagine three thousand Persian lancers, thundering up to a wretched little earthen wall, guarded by not more than a thousand terrified, pathetic, wretched infantrymen. They sweep the enemy aside, right? Like an avalanche! Well, not exactly. There are problems.
First, each cavalry mount has been hauling a man (a large man, more often than not) carrying fifty pounds of armor and twenty pounds of weapons — not to mention another hundred pounds of the horse's own armor. At a full gallop for half a mile, in the blistering heat of a Syrian summer. So, the horses are winded, disgruntled, and thinking dark thoughts.
Two — all hearsay to the contrary — horses are not stupid. Quite a bit brighter than men, actually, when it comes to that kind of intelligence known popularly as "horse sense." So, when a horse sees looming before it:
a) a ditch
b) a wall
c) lots of men on the wall holding long objects with sharp points
The horse stops. Fuck the charge. If some stupid man wants to hurl himself against all that dangerous crap, let him. (Which, often enough, they do — sailing headlong over their horse's stubborn head
It was the great romantic fallacy of the cavalry charge, and Belisarius had been astonished—all his life—at how fervently men still held to it, despite all practical experience and evidence to the contrary. Yes, horses will charge—against infantry in the open, and against other cavalry. Against anything, as long as the horse can see that it stands a chance of getting through the obstacles ahead, reasonably intact.
But no horse this side of an equine insane asylum will charge a wall too high to leap over. Especially a wall covered with nasty sharp objects. And there's no point trying to convince the horse that the infantry manning the wall are feeble and demoralized.
"Is that so? Tell you what, asshole. Climb off my back and show me. Use your own legs. Mine hurt."