Why do we believe that the 1960's are best understood not as an aberration, but as an integral part of America's history?
If we believe this, it is because we see American history (at least in part) as a continuing process of trying to improve the country and the society. In the 1960s, there were many movements that were trying to do what they thought would improve society. This was an unusually busy period for such movements, but it is in no way unique or aberrational.
For example, both the 1830s and 1840s and the early part of the 1900s (the Progressive Era) were times in which major reform movements played a huge part in American society. These were times when people pushed for abolition or women's rights or prohibition. Because such efforts at reforming and improving society are so common in US history, the 1960s were not an aberration.