Here's how banks counterfeit money. You deposit $100. The bank loans out $80 of your money to someone else. They put that money back in the bank. The bank now has $100 - all your money. But your checking account says $100, and the loanee's checking account says $80, for a total of $180. The bank has now effectively created--that is, counterfeited--$80 in new money. They gave this new money to themselves, and then loaned it out. Since their reserves are still over 20% (or whatever the present reserve requirement is), they keep doing this until they have stolen control over 80% of the money.
I'm curious about your reasoning and whether you actually believe it. Say I am short on cash right now, maybe I get paid next week and am hungry today. So I give someone an IOU for $20, payable to the bearer in two weeks, in exchange for $18. The $20 IOU is new money. Have I counterfeited, in your view?
The $100 in your checking account is an IOU, stating that the bank owes you $100. It is an IOU that the bank fully intends to repay, has made reasonable arrangements to ensure they can repay, and barring unusual circumstances, that they actually do repay. No fraud is involved. Nothing is claimed to be something that it is not.