Between 1955 and 1968, african. Webtoday’s social movements are grappling once again with a central challenge for the new left: How to remedy injustice while maintaining vitality and independence. Webdiscuss how and why various groups of people within american society began to challenge and criticize the nation’s way of life in the 1960s. Webdiscuss how and why various groups of people within american society began to challenge and criticize the nation’s way of life in the 1960s.