You don't "own" your own debt. The bank / other entity you are indebted to "owns" the debt, hence why they can sell it to a debt collector for pennies on the dollar. Instead of owning your debt, you are liable (or there's a better word than "liable") for your debt. Basically, you already "sold" your debt when you first became indebted.

It's not really a dumb question. I get why people might look at their debt as something they own, given the debt itself is tied to their identity and credit score until paid off.

You write your name on a piece of paper that says -

"IOU so much money"

and then you take money from anyone who's willing to give you money in exchange for that paper.

Debt = that paper

Selling = basically getting money for that paper

"Selling debt" is a euphemism for "selling bonds".

What you do is invent the phrase “as good as gold”. Then you convince the world that your paper is more valuable than theirs, and they store it in their vaults instead of gold. That’s how you export inflation and sell your debt to suckers.