for one, parents have a different incentive structure than teachers do

while parents aren't perfectly incentivized, they have a larger stake in you growing into a happy and healthy adult than teachers do

I believe that this (for want of a better phrase) perfect economist picture of parents is so swamped by culture and superstition and politics and all the rest of it that it's effectively invalid.

Many parents do want their children to be happy and healthy, but I believe the number who do this because they assess what their stake in "Project Children" is and conclude that their expectation value is higher with happy healthy children is vanishingly small.