The problem is the Chinese belief that they can separate the EU from the US, which they largely cannot. See, Chinese strategists think in terms of rational interests, believing others to be like themselves in wanting to advance their position in the great game. They think the problem is the US, and only the US, when in fact, it hasn't played out that way.
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Since China's modern values are fundamentally incompatible with that of the West's, there's not much to realized, ultimately, in courting Europeans.
You're right about them projecting their own thought process/culture onto others. It's one of the biggest problems with China.
The central problem is race/racism. It has nothing to do with values.
human rights - us/eu are genocidal mass murders and serial rapists who impoverish people through the imf/world bank debt traps vs China respects human rights and tries to give people a better life with BRI.
freedom - see above. no freedom when you're military occupied or dead or starving because of white neo-colonizers
democracy - us/eu has oligarchy disguised as a democracy vs people's democracy
free press - both have high levels of censorship
free speech - us/eu has more but the difference isn't that big.
religious freedom - same
property rights - us/eu steals lands, steals people, steals national treasures, steals gold, steals foreign reserves, steals your assets, steals ip (toshiba, alstom, tried to with Tiktok), steals by exporting inflation so even your savings or not safe vs actually respects property rights
rule of law - endless white police brutality, lie to invade nations, have law called the Hague Invasion act to prevent international law from bringing justice, crippled the WTO because they're losing vs actual rule of law
If it's really about "western" values they would abandon each other and partner up with China, but they won't because they are a gang of sadistic white racists who will never change. They've had 500 years to change, but every one of them with power choose the path of racist genocidal evil every time.