People shampoo should not be used on dogs because the pH levels of the skin differ, and it can be too harsh for the skin and fur of a dog. Dog shampoo is formulated for the pH balance of a dog's skin and is the recommended product to use.
People shampoo can strip the natural oils from the dog's coat, which can cause dryness and irritation. This is more likely to happen if a dog is washed with people shampoo for a prolonged period of time. The fragrances in people shampoo can also cause irritation of the skin of a dog if used on a regular basis.