Graves' diagnosis as to why chicken demand has fared better than beef demand?
I suspect he's partially right. Fat concerns probably explain part of the decline in the 1980s and early 1990s. But, there is another major part of the story: relative prices.
If beef and chicken are demand substitutes, then a fall in the the price of chicken will cause people to substitute away from beef toward the lower priced chicken. This will result in a fall in the beef demand index (or at least make the index smaller than it would have been otherwise).
So, what's happened to the retail price of chicken compared to beef since the 1970's? Here's the retail price of beef divided by the price of chicken according to USDA data.
In the early 1970's, a pound of beef was about 2.5 times more expensive than a pound of chicken, and this figure trended upward over time. Today, beef is over 4 times more expensive than chicken.
The lesson here is that increased efficiency of chicken production, resulting in lower relative chicken prices, has led to an increase in chicken consumption and reduction in beef demand.