Why is the shark not a mammal?

Alright, so because a Shark is an animal it's Kingdom- Anamalia. Because it has a basic skeletal structure (Cartalidge, not bone) it goes into phylum chordata. Although, instead of being placed into the class mammalia like an elephant would, it is placed into the class chondricthyes, which is one of three classes of fish (The other two being Ostychthyes [Bony Fish] and Agnatha [Jawless fish]) that contains sharks and rays. It belongs here instead of mammalia because it's a fish, it lays eggs, has no fur, does not produce milk, etc. Look up what makes a mammal and you can compare them.