There are many arguments for accommodationists, but the Creation/Evolution argument fundamentally points to the object of one’s faith.
The evolutionist attempts to justify age in terms of billions of years by using relative metrics, all assuming constants only measurable in our local space and time. Hs argument has no gauge to justify his leap of faith identifying relative deduction as absolute value.
Even radiocarbon dating techniques sloppily hinge upon huge exponential relationships, which easily may be swayed by millions to billions of years depending upon how they are framed.
Provided the dating techniques are consistent, they have local relative value to indicate relative differences in age. i.e. this rock is older than that rock in its present chemistry and structure. They might relatively quantify those differences. e.g. this rock is 1.8887 times as old as that rock.
Identifying the rock as 1.2 billion years old, or any age beyond human history of about 6000 years is prone to error.
Radioactive decay happens at a constant rate, which we can measure. Given a specific radioactive compound, we can precisely measure the quantity of its decay products and calculate from that how long the decay has been taking place. As long as there is still radioactive starting material, that length of time calculated is the age of the object being dated.
We express exponential relationships in terms of logarithms, all of which have a linear phase, which closely approximates the linear slope equation, y = ax + b. Within that linear portion of a logarithmic curve, radiometric dating methods are extremely accurate. The large errors only appear outside of the linear portion of the curve.
human history goes back well before 6000 years
Just a recent story that appeared last week