If I had to summarize the entirety of Ray's dietary philosophy in one sentence it would be to reduce stress. And by stress, I mostly mean the stress hormones, which include the catcholamines, cortisol, estrogen (of all types), serotonin, and pituitary hormones.
You need adequate carbs and protein to achieve this. We also want to avoid gluconeogenesis, since that involves a release of cortisol.
The controversy starts with the Essentiality of EFAs. Peat says that the essentiality is not adequately proven, and that the Burrs' experiment is flawed. Essentially, the symptoms of "EFA deficiency" are the same as that of a deficiency of vitamin B6, which was as yet undiscovered at the time.
Another issue is that you get approximately 2% of calories as unsaturated fat even without trying, unless you're eating specially PUFA free lab prepared food. So you're unlikely to get "EFA deficiency" on a normal diet anyways.