Privatization helps people who can afford to not be in a situation where they are choosing between only shitty options. The point of a (good) public system is that it’s a consistent, good baseline for ALL people regardless of their socio-economic status.
So in your example, sure, if you can afford it you can put your kid into private school or simply move but what about your neighbors? Can they as well? Society functions best when everyone has fair equity.
But but the real issue is them being exposed to drag queens!