Well, shall we see how we can classify things?
1) Are you made of complex cells with internal organelles? If so, you are a eucaryote.
The alternatives are to be a procaryote or to be an archaebacterium. Both of those are single celled.
2) Do your cells have membranes made of lipids rather than walls made from glucosides and are they surrounded by an extracellular matrix composed of collagen and glycoproteins? Then you are an Animal.
Alternatives here include Plants and Fungi.
3) During embryo development, does the blastopore (the first opening) become the anus? Then you are a Deuterostome.
The alternative here is to be a Protosome, like insects, for example.
4) Do you have a head, backbone, brain, red blood cells, and kidneys? Then you are a Vertebrate.
There are a large number of types of invertebrates.
5) Are air-breathing, have hair, three ear bones, sweat glands, the ability to regulate internal temperature and specialized teeth? Then you are a Mammal.
Alternatives are to be various types of Fish, Amphibians, or Reptiles (there are many different classes of Fish, by the way).
6) Do you lack an epi-pubic bone and do females like you have a uterus which produces a placenta during pregnancy? Then you are a placental Mammal.
Again, alternatives are the Marsupials
Now, these seem like definitions that are based on easily tested characteristics of the specimens involved.
Except that by reasonable classification schemes like above, we are not in a class of our own. We are squarely in the category of Placental mammals.
Yes, and those are relevant for the later aspects of classification. Sophisticated brains happen in other animals, but are not relevant for most of the classification tree. Standing upright is a relatively minor variation. Our bones reflect that change. But you do get a few things wrong.
Other animals see colors, some see much more than we do. For example, we only have three types of color receptors while ducks have seven. A duck can see more variety of color than a human.
Other placental mammals have families and raise their young for extended periods of time. And yes, we do have hair. That is one of the characteristics of mammal.
I can also go on and on.