Why can't the political culture and system unable to handle such move
1. Because of what politics is in any culture - not just in China or the West.
Politics is a civilized substitute for war. It's a "social construct" , or better yet a "behavioral phenotype of populations", which emerges through natural selection from a less sophisticated form of behavior because it allows for greater degree of social complexity which results in better ability to adapt to changing environment and therefore better fitness. From there you have the "survival of the fittest".
Elections replaced wars because the first culture which replaced civil war with elections became capable of greater degree of competitive cooperation. Humans could cooperate together because their competition did not result in bloodshed which would immediately end the cooperation.
Short but necessary digression: Humans compete all the time for reproduction. Even parents and children do it to some degree. We are not aware of that because this dynamic exists very far away from the typical conscious mind but it governs everything about our lives - including the conscious mind itself. We are gonads (testicles, ovaries) with brains for better use of gonads not the other way around. And that's without including the memetic part of evolution which I will omit for simplicity. Therefore even if you cooperate you compete. It's in your genes. You can't help it. You can only make it more sophisticated, more oriented for long term effects, more constructive as opposed to it being a competition that is primitive, short-term focused and destructive like among most animals. Therefore humanity can't ever "end war" but it can evolve war into a non-destructive contest.
End of digression.
State is centralized violence. State is not a "good thing". It's the exact opposite. It's all the worst traits of human society put into one place, bound together by rules and conventions and thrust into full view. We can't ever resolve the evil that is part of our nature but we can manage it better. Societal evolution is all about "managing it better" than our primate cousins.
Because of that state also attracts predators or more precisely the predatory traits in human behavior. Politicians are not good people. They are the next-to-worst (the worst refusing to become public on principle). They are the power-hungry, the ruthless, the cruel. We put them in one place and say "we're going to give you some of what you want but only if you do something for us." This way we resolve their negative traits with benefit to society because they do things that most of us won't do. Western societies are the best evidence that even in democracies people just don't want to do politics.
It works like this: Imagine an excited child which runs around the house breaking things. You can either close it in its room and wait as the room is inevitably demolished or you can give it a stick and tell it to go to the fields and chase off the birds eating the newly planted seeds. One is counter-productive. The other is not. The families which lock their children in their rooms have to fix the rooms. The families which send them to the fields end up with better harvest.
Politics is the same. But it only works for as long as we re-direct those impulses. If you change the rules of the game from cooperative competition to direct competition you get civil war. You get the Cultural Revolution which was a destructive, insane attempt by Mao to regain power which he rightfully lost as a consequence of his incompetence earlier on.
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2. Because men and women compete differently
Everything in human behavior is about reproduction but female and male aspect (sexes) have evolved with different strategies.
Male aspect embodies active physical or mental fitness which is then displayed through various behaviors allowing for resource acquisition. Female aspect embodies passive physical or mental fitness which is then displayed through phenotypic traits.
Females refine the genetic pool into its best possible shape. The ideal female is the ideal genotype for both male and female offspring.
Males introduce change. The ideal male is the best new adaptation for both male or female offspring.
Males seek best existing traits for their offspring. Females seek best adaptations for the offspring. That's because male strategy is quantity and female strategy is quality. It's a misconception that "men want body, women want money". Females want traits which resulted in money and males want traits which resulted in body.
The above could be reduced to "male power is strength" and "female power is sex". And that means that both male strength and female sexuality can be used for violence. And while for males it seems obvious it is counter-intuitive for female violence. That is until you realize that your organism is built to respond with highest priority to sexual cues and an attractive woman displaying her sexuality is causing stress to men by just being in their presence in the very same way in which an aggressive threatening male is causing stress to a woman by simply being in their presence. Women can do much more harm with expressing their opinions than men because female opinion manages direct competition between men. "You couldn't beat him" is a challenge that is understood implicitly to be rewarded with sexual favour.
This is also why humans evolved courtesy, social norms, clothing etc - to manage those stimuli and reflexes. And this is why every single society "oppresses women". It does- it oppresses female predators much like it physically eliminates male predators. Men can be culled. Women can't because of reproductive limitations. So we kill bad men but only "oppress" bad women.
Women also victimize their prey by playing victim.
Think about justice as a system of balanced actions and consequences. When a criminal harms someone we restore that balance through punishment of the criminal or restitution to the victim. When a criminal harms someone and there's no restitution or punishment we talk about "injustice". But the same happens when someone is punished or restituted without harm being done.
Male and female strategies evolved to utilize the opposite extremes. Male strategy is to victimize the target without consequence. Female strategy is to gain victim status and lay blame on the target without harm being done.
The funny thing is that older cultures - both hunter-gatherer and agricultural - would understand this intuitively but modern cultures are confused because of the disruptive influences of industrial revolution and contraception.
The problem here is that we can't "solve" female predation without returning at least partly to "outdated" customs. They evolved for a reason. Industrial revolution put it on its head. Unfortunately all industrial age ideologies got confused about the role of men and women. Capitalism and socialism alike think they are equal. They're not. They're yin and yang. They are mutually supportive balance that propels our ecology forward. Until we return to that there is no "solving" to female aggression entering in direct conflict with male aggression.
Now I am not saying that we have to return to the past. I'm saying that the past had an understanding of human nature that was simpler and yet more correct. We know infinitely more today and yet somehow draw all the wrong conclusions. It's time to put the knowledge to the use of wisdom again.
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If we now put 1 and 2 together we'll see that in essence it is not a female victim being rejected by a fair and just state that should resolve the issue but a female predatory strategy in the context of political competition. China is doing the right thing by eliminating it as a factor.
They can't solve political infighting and corruption because that's what politics is and must be. When we learn how to change human nature politics will become irrelevant. We won't improve politics. We will abolish it. Until then it is what it is.
They can't solve male vs female aggression in political terms because that's inherently biological. You could as well turn the children against the parents and parents against children - and that's what we call a "pathology" and a "dysfunction" in developmental psychology.
So they isolated her. Correctly so.
When that tennis-playing trollop engaged in a sexual behavior with the CPC official she was not a poor victim. She was trying to "hunt" the high-status man as much as the man was trying to "hunt" the attractive woman. He won, she lost. Now she is being used against him as a weapon.
The reason why those matters are front and center in the West is because the political system is different in the West.
In the West consent is explicit and continuous therefore the drama is continuous - in particular because women vote and as such they are targeted with issues that have the highest emotional impact and they are obviously different than those that impact men. "The leader is a rapist" is an effective emotional strategy that is not without merit. Leaders must be people with discipline otherwise they are unfit to lead. Obviously in the media it's just smears because it's pot calling the kettle black.
In China consent is implicit and only relevant during unrest and therefore the drama is not necessary. It's destructive to societal harmony. Politics is resolved internally.
But don't be fooled. The top of the power pyramid in the US is identical to the top of the power pyramid in China as both are identical to the top of the power pyramid in the ancient kingdoms or in the primitive tribes. And all of those are almost indistinguishable from the politics in the animal kingdom - from primates to insects.
Hopefully this is somewhat instructive.