Properly defined, "primitive" means "more like a particular ancestor", refers only to individual characteristics (not whole species or lineages), and is contrasted with "derived" (not "advanced" or "more evolved").
I have covered this and other misunderstandings of evolutionary concepts in various articles and I try to clarify these in my courses. But the intuitive interpretation in which one species is deemed more primitive than another is very hard to shake, including in the scientific literature.
This is the duck-billed platypus, Ornithorhynchus anatinus. It is a mammal, but as a monotreme it also lays eggs. It has fur and produces milk, but it does not have nipples. Because of these features, it is often considered a "primitive" species and people often compare features of the platypus to those of placental mammals in order to draw conclusions about the evolution of "modern" placental mammals.
It's true that platypuses lay eggs and lack nipples. They also have a bill, can sense electric currents in the water, and (in males) have a spur that delivers venom. Does this mean that the ancestor of platypuses and placental mammals had bills and venom? No, it doesn't. That's because these are derived traits that evolved in the platypus lineage after the monotreme and placental mammal lineages diverged from a common ancestor.
There is no such thing as a primitive species, only primitive or derived traits. The platypus, like every species, is a mixture of the two. As such, comparing it with other living species of mammals does not automatically tell you anything about what the ancestral mammal was like.
What about the claim that the monotremes are an "older" group of mammals? It's possible that, as a recognizable group, monotremes appeared before placentals. However, the lineage of which the modern platypus is a representative and the lineage of which humans are a representative have been evolving for exactly the same amount of time. This is simply a result of the fact that they share a common ancestor at some point in the past. The two lineages diverged from this ancestor and then began evolving separately. Some traits found in the ancestor were maintained in the platypus lineage, others in the human lineage, and in both cases there were new features that evolved that were not found in the common ancestor.
The take-home message is this. You can't consider one species "primitive" and another "derived" and assume that any given feature in the former was found in the ancestor of the two. You need more information before you can interpret the evolutionary history of a particular characteristic.