In the case of a country, the value backing its currency is (roughly) the strength of its economy and the size of its GDP, or all the goods and services it produces.
If our economy grows, our dollar stays strong compared to other country’s currencies. But if we just started printing paper, the value of those dollars would fall and we’d see prices rise at the same rate.
So printing more dollars might help you pay a debt that was incurred in “old dollars,” but everyone would get hurt. People holding debt would lose because they'd get paid in worthless currency. Consumers would have to go shopping with a suitcase instead of a wallet. And the U.S. Treasury would have a hard time ever borrowing again. So as bad as deficits and debt are, inflation is worse.