The design backlash of the early 1960s was against the overly-colorful and flamboyant 1950s. Just think of a pink 1950s Cadillac and you will see what I mean. It's as if the 1950s ended in 1945, at the end of World War II, and everyone just shouted "let's get crazy!" Again, take a look at the tail fins of a 1958 Cadillac if you don't believe me. Now that was crazy.
1950s design began to die in the early 1960s. Take a look at early 1960s architecture and you see a much more refined, sedate (some would say boring today) look. Graphic Design was influenced by the Swiss. Fonts like Helvetica came into wide use. Flamboyant curves were tamed into straight lines on cars, and buildings.
Of course, the backlash against that started in the late 1960s, with the psychedelic era, which lasted through the 1970s. The backlash to that was to get back to the earth, and be more "real", which is why earth tones (like brown and "avocado") got so popular in the late 1970s and early 1980s.
People who argue about "timeless design" are usually just backlashing against whatever has recently gone out of fashion. Luckily, for designers, it's always changing. Good for the business of design!
Above - Los Arcos Mall in the early 1970s, Scottsdale, Arizona. Those very modern lines look just a bit dull to the eyes of people nowadays!