Dollars enter the economy when the Federal Reserve creates reserves out of thin air and trades those new reserves for treasuries or other assets.
Dollars are destroyed when the Federal Reserve sells off assets on its balance sheet.
Taxation plays absolutely no role in this process. The Federal Reserve controls the monetary base. This would be true even if the federal government levied zero taxes.
> Governments don't need to tax in order to spend, they are the issuers of the currency.
Governments can earn revenue entirely from selling bonds or printing money - you're absolutely right that they don't need to tax in order to spend. However, this statement doesn't back up your assertion that governments destroy money through taxation.