Why might the wealthy, elite people of a country protest against universal education?

One of the characteristics that all of the countries that have high inequality levels have is the great gap of difference between education levels among its citizens.

Wealthy people have the chance to enroll their children (and themselves) in private schools who will guarantee a high standard of education. However, the public education system is usually of very low-quality standards. This results in poorly educated citizens who will become dubiously qualified workforce in the years to come.

This is a great advantage for wealthy people as they have greater opportunities in the labor market and for business as they are more qualified and have the chance to thrive.

they dont want others to compete against them