you would have to show that there was a group of people who were going to be severely harmed by the continued operation of the schools in such a manner who did not agree with the decision, and that those people had no other options (private schools, homeschooling, etc.).
I think such an interpretation of democracy will ultimately work against the very notion of "society". It will tend to eliminate all types of social welfare: sure, any lower class parent could theoretically homeschool his child. In practice most of them will not, and the children will reach adulthood with no education and no other prospects except harsh manual labor or criminality. This reinforcing cycle will eventually lead to a highly polarized society, similar to capitalism during the industrial revolution.
Conversely a 90% tax on revenues in excess of 100.000$ a year will pass, leading to severe economic contraction and explosion of tax evasion. Can you argue that the minority of high earners who don't agree with the decision have no other options ? Of course not, they are free to earn less or donate their excess revenue to the poor. Their high revenue minority status is a choice therefore by your reasoning they can't claim protection against the abuses of the majority.
Besides protecting actual minorities, an important issue of public policy is creating an inclusive social contract in which the individual choice is maximized. A country where poor people get school subsidies and rich people pay acceptable taxes is a better one for both the rich and the poor. If each policy is decided on the spot by the largest minority the social contract breaks down. Spending more on roads is not a thing that should be decided by counting how many drivers there are among the populace, rather it's a complex political compromise that cannot be decided at the individual level. It's a collective game therefore the best solutions are negotiated collectively, and representative democracy is the bargaining tool.