Great question, one that has entertained philosophers and scientists for centuries. Mammals are a group of back-boned animals, the ancestors of which lived on land and were quite small (mouse-size). These small early were warm-blooded, produced milk for their babies, had three bones in their middle ear, fur, and dozens of other distinctive features. Over evolutionary time various groups of mammals have become larger and some have became specialized for living in water (both fresh and saltwater). The most specialized of these aquatic mammals never leave the water their entire lives. Aquatic or amphibious mammals include (but are not limited to), otters, manatees, pinnipeds (seals, sea lions, walruses), and, most famously cetaceans (whales and their kin). So...humpback whales (a kind of cetacean) are considered mammals because they are one of the many thousands of descendants of the "original" mammal all those many millions of years ago. That's exactly the same reason that you, Kris, are a mammal --humans are ultimately directly related to that first mammal in the way that the humpback whale is.

Whale mothers have milk that their baby whales drink.

One summer I worked in a lab that did research on the milk of different animals, including whales. I had to give a talk about my research. Someone asked me, "Where did you get the milk?" I figured it was obvious that milk came from female mammals, so I said. "I got the milk from the freezer in the basement". The other students thought that was funny. They laughed.

When we think of the ocean we think of fish, but there are things besides fish living in the ocean. For an animal to be a mammal it must be warm-blooded, have hair, breathe air, and feed its young with milk.

Most mammals also have live babies rather than lay eggs. Whales actually do have hair either at birth or right before birth. Humpback whales need to go to the surface to breathe air every 15 minutes or so. They are also warm-blooded, feed their young with milk, and have live babies. Since humpback whales meet the definition of a mammal, they are a mammal. On a separate note, we think of birds when we think of flying animals, but bats fly and they’re mammals too!