As kittens, most mammals, including human, drink milk produced by their mothers. While it may be thought cats, like humans, continue drinking milk through adulthood, this assumption is false.
Most cat lose ability to digest lactose, a kind of sugar in milk, after they stop exclusively drinking maternal milk after weaning; approximately between eight weeks and eleven and a half months of age after birth.
Even in cases where cats can digest lactose as grow up individuals, too much ingestion or frequent milk intakes will likely still cause diarrhoea due to stomach inflammation.