There are a few things the public must understand about the use of animal models in biomedical research. Models are approximations. No scientist will dispute that. Approximations are never perfect, but they can be improved when discrepancies between animal and human studies are revealed and the reasons understood. This is what allows scientists to continuously develop increasingly faithful models of human disease.
It is unfortunate that Dr. Greek selectively quotes scientists out of context throughout his book when they acknowledge some failure of animal models and appears to imply their statements support his contentions that animal research will never lead to cures for human ailments. This is just not the case.
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I will give a specific example. In the first few pages of the book Dr. Greek quotes a major expert in cancer research, Dr. Bob Weinberg, Director of the Ludwig Center for Cancer Research at MIT, well-known for his discoveries of the first human oncogene, as saying in a Nature news article that “there is laundry list of problems with mouse models of cancer research”. This is an accurate quote, but is one taken completely out of context. In the very same article Dr. Weinberg went on to explain how such problems are being addressed by refining mouse models of cancer. 
Just to make sure my interpretation of Dr. Weinberg’s position was correct, I sent him the relevant passage from Dr. Greek’s book and requested his feedback. Here is what he had to say (reprinted here with his permission):
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“This is clearly a willful and intentional misreading of my intent, since my words were clearly intended by me to indicate that, while mouse models have their limitations, they are by far the best thing we have at present and in the foreseeable future. Indeed, they are indispensable for much of contemporary cancer research.
I would emphasize in the strongest and most unambiguous way that as we begin to develop therapies that are increasingly effective in dealing with cancer in humans, we come to appreciate, with ever-increasing clarity, that many of the properties of cancer cells and tumors cannot be and will never be approximated by in vitro culture models, i.e., in which one studies cancer cells growing in the Petri dish. For example, it is truly absurd to argue that it is possible to study clinically important processes such as tumor invasiveness into adjacent tissue and tumor metastasis without using an animal model. I am disappointed that anyone would espouse such a point of view, even for a minute! “
and he concluded:
“If the American people wish to support Dr Greek's agenda, then they must at the same time give up the hope that future biomedical research will improve the powers of medicine to treat and cure disease -- it's as simple as that."
When Dr. Greek writes in his article that “Instead of using mice, scientists could study humans with cancer and the cancerous tissues from those humans. What a novel idea; study the species you want to cure.” He seems to be implying that nobody is actually studying human tumors. Again, here is Dr. Weinberg:
“Dr. Greek says the silliest things, [...] implying that people are not studying human tumors, and implying that the kinds of experiments that one can do in mice can be done as well in humans -- truly mindless! “