It leads to other examples being used that just are not true. Like: "It is similar to a person using his or her credit card for a purchase (rather than cash, check, or a debit card) and not paying the full credit card balance each month".
I cannot sell access to my debt to pay for past debts, which is how the government has paid it's debts since 1837 (probably so long ago because that the last time we sought to destroy debt and not pay for things by monetizing debt, it caused the longest depression in American history due to Jackson's monetary policy in 1835). Nor can I create credit out of thin air, by buying treasuries my member banks. Also, I most definitely do not owe 50% of my non-intergovernmental debt to my own central bank and state and local governments and their pensions. Much less, all the while operating with a currency I control.
So yeah, I don't love it, but I get it.