You do understand the concept of a half-life, don't you? That means that even after millions of years, there will be trace amounts of C-14 left in a sample.
I am not a young-Earther, not even close, but starting with a pure C-14, after half a million years, there is less than 1 atom per mole remaining. That’s a drop of over 24 orders of magnitude, to essentially undetectable levels.
For there to be detectable amounts of C-14 in coal and diamonds and oil, for that matter, there has to be another mechanism replenishing it or it has to be younger than the age claimed by traditional geology.
However, there is plenty of radiation inside the Earth to provide this mechanism. The processes described above whereby the C-14 is replenished are probably sufficient to establish an equilibrium at some level for buried organics.
On the other hand, for a young Earth, the oldest stuff should still have around half its original C-14 in it (for a 6000 year old Earth). That is clearly not the case. And there is some evidence that C-14 generation from cosmic sources is not constant, with occasional periods of much higher levels being generated, which would give the impression that things are younger than they really are.
In any case, the point that C-14 dating is only valid for relatively recent time periods is the most pertinent, with a maximum range in the tens of thousands of years, not billions or millions or even hundreds of thousands.