Riding a horse or donkey going up a block can cause stutter and damage the animal

Riding my horse up any block, half slabs and whole ones, would sometimes have me getting stuck on the edge. After riding around with this for a little, dismounting my horse caused it to take a decent amount of fall damage. I rode around with my donkey and the situation was the same. It took some fall damage when I dismounted, after riding up some blocks.