That's not true. During slavery blacks jumped the broom and did their best to maintain nuclear families. For nearly 100 years after slavery blacks actively formed nuclear families. Most of that time the marriage rate for blacks was higher than that for whites. This despite the fact that there were fewer black men to marry.
For several decades whites were more likely to be single than blacks. Even though blacks were far more likely to be widowed, the percentage of married blacks was nearly the same as whites, occasionally slightly higher.
See Table I for census data on black and white marriage percentages 1890-1920
http://www.irp.wisc.edu/publications/focus/pdfs/foc121e.pdf
It was not until 1950 that there was a noticable increase in female headed households. The author in the above link thinks that it was due to urbanization. He may be right, there would be a wider selection of potential new partners in the city compared to the country.
The black family declined rapidly starting in the 1960s with the sexual revolution, civil rights/women able to get decent paying jobs, feminism, no fault divorce in the 1970s, welfare. In the early 70s black activists and clergy demanded that the government enact tough drug laws which of course further damaged the black family and created a greater man shortage.
Timeline: Black America’s surprising 40-year support for the Drug War