No, whales are mammals, just like you, me, your dog or cat, and pet rat. Mammals are different from most other animals in being warm-blooded, having three bones in their ears, and producing milk for their babies--among many other distinctions. Most mammals live on land, but some kinds of mammals have become specialized for living in water, whales being the most famous example. Seals and sea cows are other examples. The ancestors of each of these groups (whales, seals, sea cows) originally lived on land. Fortunately, I've been able to answer your question without going into what a "fish" is. Believe it or not, that's much more difficult to explain.

Whales are mammals, like we are. They breathe air and nurse their young with milk from their bodies.

One summer I did research at a university on the milk from different mammals. One was whale milk. When I gave my talk, they asked where I got the milk. I figured it was obvious that milk comes from mother animals that are feeding their young. So I said I got the milk from the freezer in the basement. The other students laughed.

No; whales are mammals. They are related to hippos.

Whales are actually mammals, not fish, even though they live in the ocean! All mammals are part of the class Mammalia. A class is a category of living creature that biologists use to organize different animals according to their features and evolutionary history. Even you and I belong to the class Mammalia. However, within classes there are other subgroups. Although you and I are both mammals like whales, we do not belong to the same subgroup of mammals.

The science of classifying living creatures is called taxonomy. In general, living creatures are classified into different Kingdoms (like animal, plant, fungus, and so on). These Kingdoms are separated into different Phyla, which are separated into different classes, which are separated into different orders. Orders are then separated into Families, where are then separated into Genera, and finally into Species. Within each of these categories, there are sometimes further sub-groupings. Whales are a subgroup of the order Cetartidactyla. This subgroup is called an Infraorder. Whales belong to the Infraorder Cetacea.

However, there are some misnomers which can be confusing. Misnomer is a word for something which is called one thing but means something else. In this case, there are animals which are called whales but are not Cetacea. For example, the whale shark is a type of shark, not a type of whale. Sharks belong to the class Chondrichthyes rather than Mammalia. Chondrichthyces is the class containing cartilaginous fishes.