Me spending more time with my child doesn't take away from what other children receive. If I wasn't working with my child, then I certainly wouldn't be working with all of them in place of that.
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.)
It’s similar to the tragedy of the commons… people acting in their own self-interests (better education for my child) create a situation that is worse than if we had a collective strategy (we all get a decent education, and get to share a better, more educated society.)