There is a sort of parallel "national" church that exists in China, although it contains validly consecrated bishops and validly ordained priests. The Chinese government wants to be able to control the Church in China, appointing or at least vetting the bishops itself, and the Church is insisting that this is the prerogative of the Church alone.
A similar situation existed with Henry VIII and the state church he created. What the Vatican is trying to do now is prevent the creation of another national/state church not united to Rome. It's a struggle; as the article notes, there are talks going on. So it's odd that the Chinese would force the issue right now.
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Interesting comparison. You're right, it does seem odd.