Earlier quoted context omitted.
There’s also the unstated purpose of beating China to setting up a base.
And what if China gets there first? How exactly would that benefit them, in a geopolitical sense? Sorry, but if I have the choice of wasting that much resources just so I can brag about it a bit sooner than my opponent, or watch my opponent do so, while I use said resources more productively, I know what to do.
Depending on where you established infrastructure on the moon, it might be pretty easy to conceal the things you're doing in space. You won't see anything launched from the other side, and anything leaving the moon is going to fall towards Earth, so may be difficult to detect (e.g. no heat signature).
The moon is also a pretty decent staging ground for the rest of the solar system, so getting there late means ceding any potential resource or technological advantages that being first might have attained.
There's also a slim possibility that there are things that can only be manufactured in low or zero gravity.
I think the last two reasons aren't a great justification, but anything that materially impacts geopolitics on Earth, as weapons systems and spying do, probably are if you think there's a credible threat that your adversary is capable of them. And that's probably a big part of why the US stopped going to the moon. The cost and risks didn't stack up when the US already had a pretty compelling technological lead, better intel, and the USSR never signalled that it was serious about going there.
China are serious, though, and the way they've vertically integrated the world's manufacturing base means they actually have a lead on the US in a number of areas. That's probably why there's suddenly a lot more urgency and credibility about claims of wanting to go back.