I have two, somewhat contradictory, responses. The first is that it is not "to be" that is the issue, it is that students very often do not articulate themselve

I have two, somewhat contradictory, responses. The first is that it is not "to be" that is the issue, it is that students very often do not articulate themselves very well, and one way to encourage them to be more precise is to take away their linguistic crutches. If you can get them to ask to themselves, "how can I say this another way?", then you've already gone a long way to improving their writing, and by extension, their thinking. My second answer is ontological. The "is a" relationship is much more useful in mathematics and computer science than it turns out to be in the empirical, social and psychological sciences, where even the ontological categories that one discusses may be disputed. Instead of saying, "a cat is a mammal", it seems much more useful to talk about statistical distributions of traits shared by or not shared by cats and other mammals. And then, very often, our categories can obscure truths, e.g. the truth that biological sex is more complicated, multidimensional and continuous, that the binary categories "is a" encourages us to use. Historically, much of science begins by creating ontologies; basic questions are "what kinds of things are they?"; but at some point they can also become crutches. I think we see this in modern evolutionary biology quite clearly, with a move toward "population thinking" rather than categorical ontologies.