I’m not discounting “white flight” which certainly does play a role, but there are also other factors at play here. Boston’s non-Hispanic white population is heavily Catholic—people of Irish and Italian descent alone comprise over 50% of the non-Hispanic white population. I haven’t been able to put my hands on hard numbers, but my guess is this means a pretty significant fraction of the white students are in Catholic schools.
Beyond Catholic schools, private education—both day schools and boarding schools—is much more prominent in the Boston area than in most parts of the country. This is an old, old tradition in New England, predating white flight. I met a lot of native Bostonians when I lived there 40 years ago, and I don’t recall a single one who was a BPS alum. Again, I don’t have hard numbers, but my guess is this takes a disproportionately high percentage of white students out of the BPS system.
As for the non-Hispanic white population generally, Boston is a mecca for college students, grad students, and recent college grads who tend to cycle through the city with a very high turnover rate. Many don’t stay long enough to put down roots and have kids, but they count toward the city’s total population, and the non-Hispanic whites among them probably pad the city’s non-Hispanic white totals without contributing non-Hispanic white kids to the school-age population. Some do stay and have kids. Of these, many are affluent enough to afford private schools, or to afford suburbs with good schools. They also tend to be well-educated and strongly education-oriented, thus more motivated than most to search out the best schools for their kids. Call it white flight if you like, but it’s a very different phenomenon than a lifelong resident of Chicago or Detroit or Cleveland leaving the city out of fear of racial change.