Well, I have a similar objection to neural networks. Human learning is fundamentally qualitatively different from contemporary neural network learning. It is simply not the case that I learn what a cat looks like by being shown a bunch of images of cats and having some meta-input that says "label:cat". Instead, I see a cat -- and a whole bunch of other things, including the environment that the cat happens to be in -- and I hear some sounds, and I somehow manage to make sense of the whole melange and sort out what a cat is and what the sound of my mother's voice is when she says, "That's a cat!, and the fact that the "cat" part of the audio stream is a label, and that it stands for this furry purry thing moving around in front of me, and that by producing some outputs that cause me to produce the same sounds from my own body I get the reward of hearing mommy say, "That's right!"
What we call neural networks today are interesting and useful, but I don't think they are even remotely close to anything interesting that the human brain does, and so quibbling over whether or not they are "essentially polynomial regression" or not is, IMHO, missing the point.
[EDIT: I had closed with "missing the point rather badly" but subsequent comments have convinced me that this extra emphasis was unwarranted.]