As to how they think that has anything to do with their points, it doesn’t of course - and the UK agreed, which is why they left. Also, because it’s not like the UK had any other choice.
Not only were the PLA and CCP massively popular because of the insane corruption and hyperinflation under the Nationalists, the ROC imposed (at the time), the longest martial law in human history [1]
Taiwan is democratic today, because of transitional justice, but at the time when the PRC succeeded the ROC in China, the nationalists led by Chiang were as dictatorial as you can get
The UK had no ready means to replace their (far more significant than anyone expected) losses, and were at the very far end of their logistics chain. [https://en.m.wikipedia.org/wiki/Falklands_War]. Which for the UK is crazy embarrassing. ‘Sun Never Sets on The British Empire’ and all.
They lost 6 ships (including 2 destroyers and 2 frigates), 24 helicopters, and 10 fighters + 255 KIA in the debacle. If the french hadn’t disabled those missiles, it would have been an even bigger mess. Do you think the UK gov’t wants to admit they got saved by the French?
If Argentina had their act even a little more together, or had even a little more commitment, there is nothing the UK could have done about it - except maybe nuke Buenos Aires. Which would probably have been a step too far, even for Thatcher.
Argentina was expecting zero resistance and got embarrassed they lost ships and soldiers too, and pulled out because it was making the Argentinian gov’t look bad.
But it was also really embarrassing for the UK. They had more losses there than they did fighting the Gulf War alongside the US.