https://en.wikipedia.org/wiki/Chinese_Lunar_Exploration_Prog...
The main hurdle is the CZ-10 rocket, which has not flown yet:
https://en.wikipedia.org/wiki/Long_March_10
But they have plenty of rocketry experience and the YF-100K engine they'll use for CZ-10 has successfully flown on the CZ-12:
https://en.wikipedia.org/wiki/Long_March_12
https://en.wikipedia.org/wiki/YF-100
(Yes, Chinese rocket numbering is weird, and CZ = Changzheng = Long March)
The reason I’m told we don’t do it today, is that we don’t want to. OK, China does, so what is the hold up that applies now?
No one is ever able to explain why now, and doubly so why when now is still in the future.
2. The institutional knowledge of working directly on the Apollo program has largely been lost in the US, and certainly isn't present in China.
Those are the unimportant pieces. The real reason is:
3. The US was actively at war with Russia. While it was a cold war (except for the proxy wars), the Apollo program had a wartime budget (spent nearly half a trillion in today's dollars), and a wartime risk tolerance (Neil Armstrong thought they had a 10% chance of not making it back).
2. Uh huh. The knowledge for 1960s tech is limited, agreed, but the tech is so much more superior now, and China as a nation has a high understanding. What does China not have that would be of any relevance?
3. Cool, China is in an economic Cold War with the USA.
I remain unconvinced.