Everything is a continuum. Humans divide the continuum up using acts of selective attention
Your generalization is quite wrong. Humans classify organisms based on the evidence in front of them. Can you show me this continuum between a platypus and some other animal? How does that fit into the "everything is a continuum" that you speak of?
"Species" do not have particularly crisp boundaries in the general case:
Uh, they most certainly have extremely crisp boundaries. Species are classified by the ability of two organisms to breed with one another. There isn't any "crisper" boundary than that. Once two lineages are different enough, it is no longer possible for them to reproduce sexually with one another. That is a quantum leap, a boolean yes or no situation (at least in 99.9% of the cases). Humans have nothing to do with defining that boundary. It is merely what we have observed and appropriately classified.