Cav is weak because it misses it's attacks often and takes speed boosted damage from moving toward enemies. Infantry is actually pretty good at landing blows on attacking Cavalry, even recruit will KO an Elite Cataphract because if hit them in the foot with the Cataphract's speed used against it . Infantry in general is very vulnerable too, but that's another issue.
@el_infante I second this, start a campaign and go recruit actual in game cav units (not Horse archers) and see how you feel about thier performance. Do they die too looters very often while leveling up? When you charge 50 of them into an enemy, do 20 of them die? How do you feel about you investment into them when they die so easily?
There are no anti-Cav units. This isn't fire emblem, everything kills everything. Ranged units will massacre everything in front of them. There are no "counters" in this game.