Look at it from a different perspective. Why is it that in Europe more of the population of the various metro areas lives in the city than in the surrounding suburbs, as compared to the U.S.? Do Americans just inherently like big houses and large lawns more than Europeans? And if they do, why didn't they move out of the city long before 1960, when it was eminently practical to do so?
That of course doesn't mean that suburbanites are racist today. After decades of suburban exodus the core cities are shells of their former selves, urban public school districts are almost exclusively for the poor, etc. There's lots of non-racist reasons, today, to not want to live in the city besides the inherent availability of lawns, etc. But given how racist society as a whole was in 1960, I think it's ridiculous to claim that the racial tension precipitated by the civil rights movement and desegregation didn't play a large role in tipping the balance between the cities and suburbs.