A demand for the average American to eat more meat would have to explain, as a baseline, why our already positive trend in meat consumption isn't yielding positive outcomes. There are potential explanations (you could argue increased processing offsets the purported benefits, for example), but those are left unstated by the website.
[1]: https://www.agweb.com/opinion/drivers-u-s-capita-meat-consum...
[2]: https://ers.usda.gov/data-products/chart-gallery/chart-detai...
When you couple this with the motivations of industrial food companies (some of whom are now owned by tobacco companies), and the research they do into the neuroscience effects of flavour, texture, even packaging of food, you'll start to spot that a push to "Real Food", and for that food to be less processed and more inclined towards protein, is more likely to result in overall calorie reduction.
One of the things that isn't cutting through on this program is saying "eat protein" is assumed to mean "eat meat", which some assume means you can eat burgers. Nope. Healthy protein is not red meat that has been fried - that's going to take a bit more education, I expect.