Humans are primates.
Primates are a category of mammal and are most prominently represented by apes and monkeys. Like all mammals, primates are warm-blooded, give birth to live young and nurse them, and have body hair. What distinguishes them is largely the series of physical adaptations they have undergone to adapt to an arboreal (tree-based) lifestyle. Not all primates are arboreal, but they all share these adaptive traits:
- Living in and moving through trees requires a greater degree of body coordination and physical agility than many other mammals possess. This has led to primates having relatively large brains for their body size, forward-facing eyes to aid in depth perception, opposable thumbs and fingernails for grasping, and a more robust set of bones and musculature surrounding the shoulders. For example, you can raise your arms above your head, but a dog can't.
- Primates are highly social, have various complex interactions, and have significant, extended care for offspring. Males and females display a large degree of sexual dimorphism (differences in body size and shape that makes them distinguishable by more than just their sex organs).
Other than humans (which technically belong to the ape group) and monkeys, other examples of primates include lemurs and several lesser-known groups.
Marsupials are not primates. All primates are eutheria, sometimes called "placental mammals," meaning that they give birth to live offspring. Meanwhile, marsupials are considered metatheria, which means they do give birth to live young but at a much earlier stage of development. Their young are then carried to term in an external pouch on the mother's body.
Since primates are just one sub-category of eutheria, it is effectively impossible for any marsupial to be a primate in terms of biological relationships, even if their physiology was similar.