There was no established platform on which those black families that opposed desegregation of schools stood. Some organizations such as the Black Panther Party or the US Organization (which were markedly different organizations oftentimes at odds with each other), were nonetheless in some agreement about desegregation because it meant that black folks would not have control over determining what was best for black communities. The very first of the BPP's ten point program was "WE WANT FREEDOM. WE WANT POWER TO DETERMINE THE DESTINY OF OUR BLACK AND OPPRESSED COMMUNITIES." In terms of schooling, this mean that black communities establish and operate their own schools with their own curricula and their own teachers, and so on. (Incidentally, the BPP was very successful in doing this on a very small scale, primarily in Oakland, CA). Similarly, the US Organization -- a black cultural nationalist organization -- advocated strongly for similar black cultural control, particularly over things like schools and school curricula. (An interesting sidenote: the so-called "Black Studies" movement in the US emerged out of a lot of the advocacy of groups such as the BPP and US, as well as public figures and intellectuals affiliated with those movements.)

Now, insofar as those black communities that opposed desegregation because of forced busing, the reasons are a bit simpler, though not much. One of the most notable cities in which forced busing caused a lot of problems was in Boston, and this Harvard Crimson op-ed addresses some of these problems pretty well: "The Failure of Busing". The author, Peter Ferrara, would go on to become a fairly noteworthy libertarian thinktank scholar, and it's important to note that he is not writing on behalf of the black communities of Boston here. That said, in his opinion Ferrara identifies quotas as a highly objectionable aspect of busing. Quotas were created based on percentages of a community or city's racial breakdown (sometimes), or seemingly arbitrarily (sometimes). They were basically district-wide mandates that a certain school must be comprised of a preset percentage of white students and a preset percentage of black students regardless of whether the community around that school was predominantly white or predominantly black. In Boston in which there were clear, oftentimes geographical or infrastructural boundaries between black communities and white communities (and Irish communities and Jewish communities and so on), this meant that some students needed to be bused miles away from their neighborhood school in order to appease what must have felt like an entirely made-up quota.

And because some schools located in predominantly black communities were much better than some other district-internal options, this meant that some black schoolchildren were forced to travel great distances away from their really good neighborhood school to attend a crummier and farther away school. (The same applies to some white schoolchildren too, obviously, as Ferrara's article points out).

So, I wouldn't say this is an "overview" or "synopsis" of the whole problem. If you'd like to read more about the more black nationalistic objections to desegregation, check out some of the autobiographies of various BPP members. David Hilliard's This Side of Glory is outstanding. Or, if you're into some seriously heavy dialectical/Hegelian/Marxist philosophy, check out Huey Newton's Revolutionary Intercommunalism and the Right of Nations to Self-Determination. And if you're more interested in reading stuff about black cultural nationalism, check out (if you can, it's very rare) a book called The Black Aesthetic edited by Addison Gayle, Jr. And honestly, the best way to generate a greater perspective on the busing issue as it relates to quotas and resistance, see how many old newspaper articles you can find online from major city newspapers in places like Boston and Louisville and Pittsburgh; places that had some pretty established black and white neighborhoods. Or, better yet, check out your city's online archives and see what you can drum up!