see, the thing is, it's not one spearman vs one rider. its four or five spearmen vs one rider, as any horse and rider who can reach a spearman to strike him is in thrusting range of half a dozen or more spears.
you can charge into the mix, and more than likey knock the frist two guys over.... but your horse will have three mortal wounds in it's chest and your going to be getting a few in a moment.
also, do not forget that for a lot of history, cavalrymen provided their own horses. a well bred war horse was easily as expensive as Full Plate armour, and often more. You wanted to look after that large an investment,
think of it this way. your average sports car might well be able, when driven at high enough speed, to snap a small tree it two. but if it was your sports car, would you try it?