It is thinner
The outer layer of a dog's skin, the epidermis, is only a few cell layers deep, noticeably thinner than ours. Less thickness means less buffer: irritants reach living tissue sooner, and moisture leaves faster once the barrier is disturbed. The coat does much of the protecting that our thicker skin does on its own.
It is less acidic
Healthy human skin sits around pH 5.5, on the acidic side. Measurements of dog skin vary by breed, body site and study, but they cluster closer to neutral, roughly between 6 and 7.5. That acidity in humans supports the skin's own balance of microbes. A dog's balance is tuned to its own, higher, pH.
Most shampoo on a bathroom shelf is formulated for human skin. Used on a dog now and then, it does no harm you would notice. Used every few weeks for a year, it repeatedly pulls the skin away from the range it is built for.
It is covered in fur
Dogs grow several hairs from each follicle, so their coat is dense in a way ours is not. Density traps moisture and heat close to the skin, which is why a damp coat that dries slowly can lead to irritation. It also means a shampoo that is not rinsed out has plenty of places to stay behind.
What this means for care
Three practical conclusions follow. Use products developed for dogs, ideally ones that state what pH they are formulated at. Rinse for longer than feels necessary. And dry the coat properly after a bath or a wet walk, down to the skin.
None of this requires anything elaborate. It mostly requires not treating a dog like a small, hairy person.