A common mistake in dog food is dogs can’t drink milk, but nobody can explain why dogs can’t drink milk. Some people told that milk was harmful for dogs and caused diarrhea. Truth: Many dogs can easily digest dairy products such as milk and yogurt, but some dogs are hard to digest, even cause diarrhea or vomiting.Dogs can also suffer from lactose intolerance just like humans.ome people told that milk was harmful for dogs and caused diarrhea. Truth: Many dogs can easily digest dairy products such as milk and yogurt, but some dogs are hard to digest, even cause diarrhea or vomiting.