He's talking about a change in the style of mass-market advertising.
I'm going to use the word "pitch" to mean "an advertiser's claim or argument, an advertiser's sales talk."
He says that in the old style, products like Ovaltine had been pitched by associating them with home and family. In the new style, the pitch is "scientific proof."
The two phrases are typical claims made for products that were (and still are) mass-marketed: dishwashing detergent and over-the-counter medicine (available without a doctor's prescription).
"Skin softness" would be a typical pitch for dishwashing detergent--the kind used for hand-washing dishes in a sink. Traditional soaps were alkaline and dried the skin. New detergents were less alkaline and had emollients and nice scents, so they could claim that it softened the skin.
"Quicker relief" would be a typical pitch for pain relievers and antacids. I believe it was Bufferin, a brand of aspirin, that used the slogan "Faster to your headache, gentler on your stomach."
You could pitch "quicker relief" by showing someone taking Bufferin and saying "Ahhhhhh! What fast, effective relief!" Or, you could pitch it by having scientists in white coats pointing to charts with "scientific proof" that Bufferin is 23.45% faster than "Brand X."
(Ovaltine is still made; it is basically a kind of chocolate-flavored malted-milk powder. Children like it because it's sweet and chocolatey. Because of the sugar it's not particularly healthy, it's basically just a kind of chocolate milk, but the company always tried to suggest that it healthy. It was very popular in the 1930s and 1940s in the U.S. It is still widely available but much less popular than it used to be).