Short-lived isotopes Th-230 and U-236 exist on the moon

Claim

The moon can not be billions of years old because short-lived isotopes exist there.

Evolution Encyclopedia Vol. 1: CHAPTER SIX THE AGE OF THE EARTH (see #21 - Lunar isotopes). Evolution-facts.org. Retrieved on 2008-06-07.

Like many Creationist arguments against evolution, this one is a mixture of truth and wilful ignorance. Here's the true part: Thorium-230 and Uranium-236 are relatively short-lived radioisotopes. If the Earth and Moon are indeed 4.5 billion years old, no trace of the original, primordial supply of those radioisotopes should now exist.
And here's the wilfully ignorant part: Both Th-230 and U-236 can be generated through radioactive decay of U-238 -- and U-238 is not short-lived. In point of fact, the half-life of U-238 is a bit less than 4.5 billion years! Th-230 is part of the normal sequence of decay products generated by U-238; as for U-236, it's produced by uranium ore whenever there's enough slow neutrons in the neighborhood.
Thus, the Th-230 and U-236 we see on the Moon are of recent origin, not part of the Moon's primordial supply, and therefore do not constitute evidence for a young Earth.
The surface of the moon is exposed to cosmic rays which penetrate the surface to a depth of about one meter and, by nuclear reactions (e.g. spallation), generates short-living radioisotopes.
A significant quantity of long-lived uranium and thorium isotopes exist on the moon, as well. Given how spontaneous fission works, one generally derives from the other.

Exclusion (fact that both substance are generated by radioactive decay is ignored)