Penguins, which swim linearly under water like seals and dolphins, which can't fly, and which seem to have fur rather than feathers are to me not birds, they are some kind of hybrid dinosaur-mammal as far as I'm concerned.
And the duck billed platypus with its...well, duck's bill, webbed feet and egg laying is not a mammal in my book, it is some kind of bird-mammal hybrid. So what, if it's got four legs!
Anyway these two creatures simply support my long-held opinion that the biologists of the late 19th and early to mid 20th centuries must have just got bored at creating all those families, classes, genuses and species, resulting in these two and some other unusual species, (like the species of shark, supposedly a fish, that gives birth to live young rather than eggs) slipping through the net and ending up incorrectly classified as birds and mammals. So by the end anything with four legs and a fur coat had to be a mammal and anything without fully developed upper limbs had to be a bird.
Penguins are not birds, I don't care what you say. And the cheetah with its dog like head and body and non-retractable dog-like claws and with no relatives in the cat family is not a cat! It is a canine!