It's something that happens accidentally. It is not really a discovery.
If you can simply harvest an animal's milk, be it a goat or auroch, sooner or later you are going to have a misfortune which results in cheese. It is literally a product of spilled milk in the right temperature environment.
Far from being a gigantic leap of faith, it is the only theory that explains the bones of Neanderthals and the teeth in their jaws. If the orthodoxy is right about those teeth chewing mammal meat at the rate of 6000+ calories a day for a lifetime, there is no way that Neanderthal teeth could look the way that they do.
The reason people would fight the cheese theory is that it is like a piece of wool and when you pull on it, you are going to find you have suddenly unraveled the piece of whole cloth that is modern anthropology. All the assumptions made by the orthodox start to appear really absurd and untenable.
Why, you ask.
If the Neanderthals survived off cheese protein as a major staple in their diet, it means herding was a mainstay of their existence. Right there, you have basically tossed a live fragmentation grenade into the maw of modern science. That is all it takes. The whole edifice begins to crumble apart into gibberish.
Far from painting the Neanderthals as supermen who traveled around in hovercraft, it portrays them in an entirely different light altogether. It depicts them as fairly placid, abundant and stable populations who really had no pressing need for fantastic innovation in their lives. There are a variety of reasons to believe that individually they may have been pretty spectacular but there would have been very little cause to develop militant regimentation of their ranks or specialization of labor. All the pressure for Homo Sapiens has been a direct result of his unending, ceaseless warfare.
If you think about it long enough, you will see a bunch of really bright people who rested on their laurels and pretty much mastered existence without much warfare for long periods of time. People essentially coasting on their own superiority. People who had domesticated all the existing breeds of animal husbandry and had so conquered famine and need that they rarely found a demand to investigate new avenues.
Now imagine these people suddenly facing a tidal wave of invasion of spear-chucking zombie hominids from the south who outnumbered them a thousand-to-one. These zombie replicants didn't need to be smart or innovate or domesticate or exercise long term strategic thinking. All they had to do was chuck spears, rape and cannibalize and they could inherits hundreds of thousands of years of accomplishments by default.
It is truly an instance of "the second mouse getting the cheese," literally. Neanderthals had fought and eliminated all the big predators, cleared the continent of most opposition, developed all the breeds critical to the foundation of larger population societies and solved all the big problems of achieving abundance in almost any conditions. They had "set off the trap" and cleared the way. All Sapiens had to do was to crawl forward and nibble on the cheese.
The explanation fits the facts because it explains amongst other things why the human brain has been shrinking for more than 20,000+ years. Their completely opposite and incongruous sexual selection criteria never selects for the same kind of brains or intelligence and they cannot maintain the windfall they fell ass-backwards into. What they stumbled into by chance they lose by design.
In terms of the r/K ratio, it also explains why the human race appears to be a blend of 80% sex-crazy polygamous war monkeys mixed with less than 20% monogamous, conservative, stable and long term strategy thinkers. It explains why everything that the 20% build up the 80% will immediately endeavor to tear down. Once you can explain this, you have explained almost everything important. Deep in his heart, Homo Sapiens is a rape ape who wants to kill everything and the Neanderthal remnant will never be able to hold the line against these lunatic creatures. That's why civilization is always in decline. Saps always has bloodshot eyes and a euphoric expression talking about "progress" and "openmindedness" because he is insane. There is nothing that lasts long with mankind for this reason. Mind you, the evidence is that the worst change-revolutionary-junkies come from different strains of Neanderthal gene expression itself (Mousterians) but it is the general madness of the Sapiens breed as a whole that makes him so receptive to all of this agitprop and so eager to listen to it's message of self-destruction. Part of his innermost essence resents all these restrictions on his "natural self" and principles of conduct that are so innate to Neanderthals. He wants to be "liberated" from whatever temporary organization that the Neanderthal remnant is able to assemble and go back to his "real self," which is a bloody vicious warlike chimpanzee who answers to no law but tooth and claw. The two breeds don't belong together and are no more compatible than oil and water in the same bottle. You can't mix them no matter how many rapists insist otherwise.