Just like WWI moved us from the 19th- into the 20th-century, the sixties framed the last quarter of the last century and, apparently, the first years of the 21st. We are still living with the after effects of that decade.
If you take any American high school yearbook from 1963 and compare it with the same school in 1968, you will see a change greater than any other 5-year period. In fact, the difference between seniors separated by just five years looks like 25 years have passed. The conception of the change of the 60's occurred the day that Kennedy was killed. Before that all aspects of American society from the church, to education, to style resembled the 1950's. 1964 was the pivotal year in the last half of the 20th-century because of all the changes wraught by everything from the Beatles to birth control to civil rights.
The gestation period ended the spring/summer of 1968 when Martin Luther King and Bobby Kennedy were killed and people saw their neighbors' kids being beaten on Chicago streets outside the Democratic National Convention. The Wall Street Journal called it the loss of "guardrails." To be most concise, the change began with the death of JFK and came to fruition with the death of RFK.
PBS did a wonderful series about the sixties about 10 years ago, which is probably available for loan from most public libraries.
That's a very good observation, but maybe the difference between 1965 or 1966 and 1970 or 1971 better illustrates the difference. I don't know if there were so many long-haired kids in high schools in 1968. A few years later, there were a lot more. It took a while for trends to trickle down from colleges and young adults to high schools. I'd say, in terms of style, 1967 was pivotal. 1968 in politics.