The resistance is because of a system tied to the end of segregation and segregated schools. Basically, when the Supreme Court ruled that schools had to be integrated, the pushback from those who opposed it was to push for more ways to ensure that they weren't funding black kids.
It basically had 2 components. The first component was people moving out of cities. "White flight" is the common term but we should actually describe the thinking process. With segregation, white and black families could live in the same zip code but not have to send their kids to schools together. With integration, the black kids could now attend the white schools. Pro-segregationists needed a way to ensure that they could maintain segregated school systems without breaking the law. The solution was to move to places where there were little to no minorities. The more expensive the new location, the more likely it would be segregated as a result of income.
This meant that they could get all-white schools without breaking the law.
The second component was pushing for township lines that put these primarily white and economically segregated neighborhoods outside of townships and cities that included the minority neighborhoods. This legal partitioning meant that the minority neighborhoods fell outside of the white towns and the minority kids couldn't attend the white schools.
Once those 2 steps happened, the township then set local taxes to fund their local schools. And the states didn't intervene because the people with the money and know how to actually implement these types of legal segregation strategies were friends with the people in power. It's all legal so there's no real judicial argument against it.
Fast forward 60 years and no one really has an interest in undoing the system for the economic reasons. The families with money have no incentive to pool education dollars and the families without money don't have the political capital to change it.
If you want a decent real life example of the situation, look at Baltimore around that time. The wealthy portion of Baltimore moved out of the city after school integration. Then they wrote laws that said no tax dollars generated in the county
but outside of the main city could ever be used for the benefit of the city of Baltimore. They effectively defunded the city.
The numbers are important here. Following integration, Baltimore City lost 110,000 residents in a decade. It decimated their ability to pay for things. This pattern happened all over the country. When people talk about cities being shitty and poorly run, they often leave out the economic destruction reaped on cities because of integrated school.
Baltimore population graph showing what happened post integration:
Chicago? Same thing, almost 1 million residents lost:
Detroit? Same thing.