Why does a platypus still count as a mammal when it lays eggs and has no nipples?

Answer: Producing milk for the young is the trait that defines the mammal group.

Nipples are needed for nursing, so an animal without them is not really a mammal. — Nipples are the usual delivery system for milk in mammals, so it is easy to treat them as the whole requirement. But the trait that defines the group is producing milk for the young, not one particular way of delivering it. A platypus mother has mammary glands and releases milk onto her belly for the hatchlings to lap up, which is nursing without nipples.

Producing milk for the young is the trait that defines the mammal group. ✓ — Correct. Milk production from mammary glands is the trait that defines mammals, and the platypus has it even though it lays eggs and has no nipples. It feeds its hatchlings milk from belly patches, so it sits inside the mammal group rather than outside it. The odd combination is a reminder that egg-laying and milk once coexisted in the mammalian line.

Live birth defines mammals, so any animal that lays eggs falls outside the group. — Live birth is how most mammals reproduce, which makes it a tempting shortcut for the whole group. But it is a common pattern rather than the definition, and a few mammals lay eggs instead. Monotremes such as the platypus lay eggs and are still mammals because they produce milk for their young.