Dogs don't get dizzy from chasing their tails. The reason why they don't is a little complicated. When dogs chase their tails, they aren't spinning. Think of them as going forward with a slight change in direction. On the contrary, humans spin rather than going forward. This spinning causes us to lose our balance and we feel dizzy. That said, dogs do get dizzy when their vestibular system is affected. The vestibular system helps a dog to keep its balance and when the system is affected by, let's say, an infection, your dog can feel dizzy.