Liberal ideas were taking over the country and change was happening in the United States in the 1960's. The Kennedy's, John and his brother Bobby, were symbols of and catalysts for that kind of change, so their assassinations in 1963 and 1968 defined the movement of protest that was infusing music and art and culture.
The Kennedy assassination defined more than just an entire decade, it defined the way we thought many decades to come. This was such a tragic event that we still remember and mourn the death of President Kennedy and his family today. Even though many people wanted Kennedy dead, it shook the world many years to come.
The 60's were probably some of the most interesting and remembered years of modern history. Yes, the assassination of JFK and Robert were two of the major events, but there was also the music, Woodstock, Vietnam, walking on the moon, MLK's I Have A Dream Speech. It is hard to just say the assassinations were what defined the whole decade. I do not believe the 60's can be defined by just one event.
When people think of the 1960's they don't immediately think of people being assassinated, even if those are highly recognizable events. The Vietnam War, the Hippie culture movement and sexual revolution/free love movement, and the Moon landing are all higher profile things that people would remember of that time period.
Both Kennedy assassinations were defining moments of the 1960s, but there were so many other moments that were as equally if not more defining. Some examples: the arrival of The Beatles in NYC which ushered in The British Invasion; the Camelot era; the 1967 Youthquake; the expansion of the Vietnam War; the sexual revolution; anti-war protests; the "I Have a Dream Speech" by MLK, and his assassination, and the most defining moment of all--man's first landing on the moon.