According to recent research by Weissbourd and Torres out of Harvard, "white, affluent parents value school quality more than integration and view integrated schools as 'educationally inferior.'" These researchers further found that school quality itself was evidenced by these same parents in the extent to which children of white, affluent parents send their children to a particular school.
"The survey findings – namely, the hesitancy or refusal of white, middle- and upper-class parents to actively choose integrated schools even when they say they value them – speak to why so few school districts have successfully tackled integration and expose the biggest sticking point in the dozens of schools districts currently trying to tackle the issue: the intransigence among many white families."
The short of it is that school integration is a great idea in the abstract, but not an attractive proposition where the rubber meets the road of actually enrolling one's child in a racially and ethnically diverse school.
A deeper analysis of the underlying governing dynamics would take a look at Cheryl Harris' notion of "whiteness as property (Harris, 1993, 2003)."
Harris, C. I. (2003). Whiteness as property. Harvard Law Review, 106(8).Harris, C. I. (1993). Whiteness as property. Harvard law review, 1707-1791.