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We stick the garden hose in and turn it on full blast.The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere.
The water level just sits there even though the hose is going full blast.
That is, the equilibrium point should have long since been reached given the present rate of carbon-14 production and the old age of the earth.
The next step in Henry Morris' argument was to show that the water level in our barrel analogy was not in equilibrium, that considerably more water was coming in than leaking out.
It's a great argument except for one, little thing.
The water is coming out of the hose at a steady rate as our model assumed!