Minecraft wiki entry for Summoning_jockeys, associated text: If the mount is a passive mob it cannot inflict its own damage, the passenger has to inflict its own damage. If you have a skeleton riding a cow the Skeleton can attack, not the cow. The only case is where the Mount is hostile, such as a spider, if can attack as well and leap (this is the only exception where a Mount can jump on its own), making it deadly for the player. A neutral mob, such as a polar bear can attack on its own if the polar bear itself is provoked.