Remember... The earth is flat... Because they said so... If you don't agree... OFF WITH YOUR HEAD!
Seems like truth goes through same steps; first hated, then spoken out against, then tried to be destroyed, then accepted by all (eventually). But this carbon dating was gladly accepted :) hmmm then how old is the moon?
Well, you are right. The validity of radiocarbon dating depends on the assumption that the half-life of carbon-14 isotopes does not change with time.
But, one of the principles of most use in scientific investigations is occam's razor, which says that when presented with a choice, usually the simplest answer is the most correct. So, it is -assumed- that the half-life was not different a thousand years ago. However, it is possible.
But radiocarbon dates have been validated by other methods (such as counting rings on big trees, for instance) and there is no evidence for any change in the half-life of carbon in the time that the method has been in use.
Also, a time-invariant half-life fits in with the current understanding of nuclear decays, so it seems pretty unlikely that it would change over time.
As for the moon, it is not a candidate for carbon dating, which only works on samples that were alive at some point - bones, trees, antlers etc.
The basic idea is that the living organism exchanges carbon with the environment while it's alive, and stops doing so when it dies. Since the proportion of radioactive carbon in the environment is fixed, then when the organism dies, it's decaying carbon-14 content stops being replenished by eating, breathing etc. So since the moon is mostly rock, and no biological processes exist (that we know of) on the moon, carbon dating doesn't work there.
So anyway, in general I agree that everyone should be a skeptic. Nobody should blindly accept something just because they are told "it is so" but should try to understand the whys and hows and come to understand it themselves! These days science is treated with almost as much reverence as religion once was.
Long ago, if the pope said something was so, it was so - and now, if a scientist says something is so, people accept it as so! Unfortunately this is just one of the fundamental problems of human nature - we often accept what we are told because it's told to us by an authority.
So it makes me happy when someone asks questions that challenge the assumptions!