Because they, like many other countries, have created an arms race. The perceived status rank of each university with its fixed number of slots and the behavior of employers, who give applicants jobs with pay and prestige corresponding to the relative status of what school they graduated from, create essentially a forced ranking of all kids coming out of the educational system. The demand for afterschool tutoring is not driven by a need to fill in gaps left by a poor daytime education but by a desire to get ahead of others in the relative ranking. This demand does not depend on the quality of the daytime education.
It is assumed that your success in life comes from your relative standing, your percentile in the forced ranking, not from your absolute level of education. Both the public and the private education systems optimize for getting their students as high on the relative ranking as possible, not for training each to be as valuable as possible in terms of what actual services he can provide to his family, his employer, and his society.
It is often assumed (around the world) that the former will yield the latter. In other words, competition for ranking will make everyone more valuable. This is only partially true, though. The ranking is a one dimensional aggregate of a few dimensions that are easiest to measure: solving math problems, answering trivia questions about English vocabulary and grammar, remembering historical facts, and so on. This causes those few areas to be over-invested in, hence others to be under-invested in, relative to their real ability to produce value for self and others in adult life.
The real economy (not just money but quality of life) is far more diverse and multidimensional. Post-primary-school education would be better if it didn't force everyone to focus almost all their time and effort on maximizing the same three or four dimensions.