"This is what I told my client and he insists that he has already paid taxes on the amount included on the 2021 return."

Show him how much was the distribution, and how much was reported for taxes on 2020. That will help you confirm you did not report all of it for that year, as well.

"I also told him that he was a cash basis taxpayer and that taxes are deducted in the year PAID!"

Nothing about this is deductible.

"Also, that taxes paid are not deferred. Taxes are taxes as stated in my second reply."

Here's a common confusion in the way we use Tax Language:

People confuse Withholding and Estimates, which are Prepayments against Likely taxes, and Taxes. The end result of preparing the tax form is Balance Due or Refund Due, based on Taxes Owed offset by those prepayments.

You see this all the time with people cheering for their Refund "of taxes" and it's simply their own money, overpaid to the IRS.