Education is about more than just your particular children. We all benefit from a society where people are better educated. (A more informed electorate creates a better society.) If the act of pulling your kid from school causes that school to get just a little bit worse, you’re making society just a little bit worse as a result.

There’s a similar reason why, in countries that have state-funded health care, you’re not allowed to seek out private doctors or private insurance. The point is to not allow the rich to siphon the best resources away from everyone else. (This is obviously very anti-capitalist, but I think for some institutions like medicine and education, it may make sense.)