Humans have belly buttons because we are mammals and give birth to live young. The umbilical cord connects a developing baby to the placenta, which provides nutrients and oxygen from the mother. After the baby is born, the umbilical cord is cut and the remaining part dries up and falls off, leaving behind a belly button.
Whales are not mammals, but rather cetaceans, which are a group of aquatic mammals that includes whales, dolphins, and porpoises. Cetaceans do not give birth to live young in the same way that humans do. Instead, they give birth to fully-developed calves that do not require an umbilical cord. As a result, cetaceans do not have belly buttons.