There are just not enough proper schools for them to attend. They have to compete for the spot to get an education. And all these elite colleges/high schools are located in Beijign, Shanghai, etc. They usually take in local students first.
So you see the problem. They will always be some form of private tutoring as long as there are immensive competition for basic education.
China needs more young people to be happy to be factory workers forever, instead of seeking out white-collar jobs.
But many young men and their parents are convinced that a University degree is essential to find a wife.
If the situation reverses to more women than men, by simple microeconomics the dating standards of women will fall and more families and men will be content in lower-status (but economically important) roles.
China could incentivize more women being born by allowing 'bride prices', paid to the bride's family instead of just being used for the wedding. Another option could be to encourage excess males to emigrate, as seems to be occurring in India.
Obviously educating citizens is good for a nation. And if it is really what people want to do, that's good. But it would also be good to ensure people can make a good living and self actualize without a formal education.
How? Wanting magic to be true doesn't make it possible. If your economy is already strong enough to provide a good living to anyone who wants to be a noncontributing poorly educated self-actualizer, then OK, let them enjoy that. But what if it's not? Who supports them? Even developed countries with good social welfare usually make it hard to be voluntarily unemployed and receiving welfare just because you'd rather play on your hobbies than work for others' benefit. It's meant for people who want to work but can't, not those who don't want to but can.
You twisted my comment into a false dichotomy. Societies obviously cannot fully subsidize people to enjoy a life of the most self indulgent or pretentious interests. But a society can acknowledge that not everyone is going to grow skills, discover talents or develop interests in the same way. Perhaps the most efficient thing is to shrink agriculture work to the bare machine assisted minimum with a dichotomy of skilled labor at the top and a balloon of grunt workers at the bottom. On the other hand, growing a wide professional class of ag workers with more stake in the system may lead to happier workers and perhaps a more sustainable and durable ag sector. If a society needs to subsidize that or create a pipeline that carries workers out of primary education into that kind of work it may be preferable for less tangible reasons. It's absurd that we should drive forward with efficiency no matter how much it emiserates people. And to insist upon it with so much of the reward for it accruing at the top is downright feudal.
Even still, it's not necessarily true that funneling everyone into the knowledge economy is in fact better. If someone would be happy and productive farming five acres but they go to the city, get half a degree, crash out and end up in a very low value labor market, society has probably lost out. It is my opinion that economists view labor markets aa far too fluid. They don't account for the fact that people are more like bits of rock, sand and clay than they are like water. They clump together, break apart and get stuck.
But people mostly seem to want to be richer and are happy to forgo that kind of lifestyle in exchange for a higher paying job. Who are we to tell them that what they want is not what they should really want?