Why does the level of radioactive carbon in the atmosphere have to be at equilibrium?
Well, under an old earth interpretation of the world, the problem is that carbon 14 is something that is (mostly) produced when the sun interacts with the earth atmosphere. If you start counting from when the planet has carbon in the air to react with the sun's radiation, carbon-14 starts to be produced, and at the same time starts to decay. The more radioactive carbon in the air, the faster it decays, until after a sufficiently long period of time the amounts entering and exiting in this fashion arrive at a balance.
Radioactive atmospheric carbon does not have to be at equilibrium according to my understanding of our world, but it is required by the old earth theory. The typical evolution theory requires an extremely old earth to allow for a near infinity of time to allow for "evolution" to happen... a process that is so slow that no one has ever observed it in action. It somehow seems more plausible if "millions of years" is prefixed to the explanations.
The entire carbon-14 dating scheme makes the assumption that radioactive carbon in the atmosphere is constant and has always been at current levels. If the earth is indeed extremely old, then this would be the expected result. But using an assumption of "old earth" (for constant C14 levels) as a way to generate numbers (from measuring C14 levels) to prove "old earth" is a classic example of circular reasoning.
On the other hand, if Carbon-14 is still increasing and has not reached equilibrium, that would be consistent with what one would expect from a young earth. I have seen evolutionists react to this before. Whereas before they insisted that C14 was constant and could always be relied on, afterwards the argument changes that now C14 must be fluxing back and forth. they figure. I suppose "unreliable" feels better than "plain wrong."
Do you remember anyone putting forth a study to make sure that Carbon-14 was both constant and at equilibrium before it was assumed to be so for the purpose of dating organic samples? Because with the wrong assumptions in place, measuring an early sample from a young earth could appear to absurdly old, simply because its world wouldn't have accumulated the present-day levels of C14.
Again, according to my theory, the pre-flood world had a different atmosphere than today's world: Genesis describes an environment with "no rain", where "mists covered the earth", and where life forms didn't age as fiercely as today. That could be consistent with a planet that was less subject (or perhaps shielded) from radiation. After the end of that flood, recorded life spans started to decrease in a nice mathematical curve, approaching today's accepted norms. (We realize today that radiation has a large effect on our aging process.)
Anyway, just recapping your question. Why does atmospheric radioactive carbon have to be at equilibrium? Because an increasing amount indicates a young earth, and a variable amount nullifies the accuracy of numbers obtained through carbon dating. The circular reasoning employed to proclaim Carbon dating reliable demonstrates the bias present within that community.