Cats are unable to teleport to their owner part of the time, especially over ice or when in water. When in water, tamed cat is unable to come back on land by climbing ice and needs a naturally-generated piece of (non-ice) shoreline to come back on land. Will not use a piece of placed sand, dirt, etc. to come back up.

Rabbits also unable to climb regular grass bricks when being lead by a carrot. Jumping and forward momentum is there, but still unable to climb the actual brick to get to the target with food.