I am not the person to answer this question, but since so many people comment to explain to posters why their question is not a good historical question (loaded with pre-existing biases, assumptions, ahistorical, essentialist, and many other flaws), I wanted to take a moment to explain to you (and anyone reading!) why this is a great historical question.

Too often, people explain events without asking this question -- E.G. why did the French Revolution happen? "Because the rulers were tyrannical" - no! The rulers had been tyrannical for a long, long time; when did the french revolution (any of them!) happen when it did?! Asking questions like this helps illuminate historical contingency as well as prompt critical examination of wider historical context. What was the economic, intellectual, social, and environmental context in which the event in question transpired???

Often, the answers can reveal surprising things. In your question for example, asking this question reveals that "the Civil Rights Movement" was actually part of a continuous strain of previously-enslaved-peoples' resistance to their oppression that traces back to slow-downs, escape attempts, etc. under slavery. This prompts further questions - why did they try new tactics in the second half of the twentieth-century? Why did they achieve more success, both legislative and (to a lesser extent, to be sure) social/cultural at this time? What were the institutional underpinnings of this formal movement, and what allies did they attract to their cause?

I know enough to give an American history survey course lecture on the topic, but will forbear providing my own answers in the hope that a true historian of race in twentieth century America comes along. Hopefully we can both learn something new--in the meantime, thanks for the great question!

I would recommend the book "Political Process and the Development of Black Insurgency, 1930-1970" by Doug MCAdam. I can give you the briefest of overviews here:

What you saw happen during the 1950s and 1960s was the denouement of a process that stretched back, at least, decades. What you have to keep in mind is that in order to succeed, the civil rights movement needed an organizational structure, both formally and informally, that would allow them to draw on the resources of the black community and it took time for those structures to develop. At the same time, they didn't face on undifferentiated monolith of white America. What happened during the Civil Rights Movement, MCAdam would argue, was that the black community was ready to act in an organized way and the opportunity landscape that they faced was finally ready for a movement. From there, you needed the right people making the right decisions about how to go about changing how the country viewed civil rights and citizenry.

In other words, before the civil rights movement you remember, blacks didn't have the same tools or the same opportunities to wield them, but they did what they could with what they had and they set the groundwork.

As others have pointed out, the Civil Rights Movement was part of a long continuation of African-American resistance. I'll try to give you a quick overview of that continuum here.

Before the Civil War, African-American activism was primarily concerned with abolitionism. After the Civil War, African-Americans began to see their rights chipped away and discrimination legislated in what is called Jim Crow. You have to remember that the rise of Jim Crow didn't happen over night. It started in the 1870's and then really spread after Plessy vs. Ferguson was upheld by the Supreme Court in 1896. So it wasn't until about 1900 that the full force of Jim Crow came into effect. Incidentally, this is about the same time we start to see a lot more organizing from African-Americans concerning civil rights and discrimination (see: Righteous Discontent by Evelyn Brooks Higginbotham). This came primarily came through religious social organizations. But their goals and methods were a little different from what we see during the Civil Rights Movement. They were more concerned with integration and creating a class of people who could lead African-Americans toward better treatment. They were laying the foundation for the Civil Rights Movement. They were concerned with educating a class African-Americans to better argue and work for equal treatment. One of the colleges created by this movement, Morehouse College ended up educating both Martin Luther King Jr., and his father.

In many ways though, it was also about the US being "ready" for a civil rights movement. The history of the US wasn't exactly ready for a civil right movement either before the 1950's. The 19-teens and 20's was a particularly brutal time for race relations (called the nadir of race relations), the 1930's was dominated by the Great Depression, and the 1940's by the Second World War. It could also be argued that the use of television had an impact on the popular support of the Civil Rights Movement since people all over the US were able to hear speeches and see what was being done. The Civil Rights Movement also relied heavily on support from the national government and the court system to help bring down Jim Crow. Because of Plessy vs. Ferguson, the Supreme Court had allowed states to create separate but equal clauses. This changed in 1954 with Brown v. Board, so it seemed that the courts were much more likely to strike down segregation/discrimination laws after this. So a lot of the momentum of the Civil Rights Movement was done through the court system and the US government, which only seemed ready to tackle Jim Crow after the 1950's.