From the “interpretation” section of the link I provided:
Truthfulness should be the absolute norm for those who trust in Christ. Our simple yes or no should be completely binding since deception is never an option for us. If an oath is required to convince someone of our honesty or intent to be faithful, it suggests we may not be known for telling the truth in other circumstances.
It’s likely that the taking of oaths had become a way of manipulating people or allowing wiggle room to get out of some kinds of contracts. James is definite: For those in Christ, dishonesty is never an option.
From the “interpretation” section of the link I provided: