Except personal debt is different than government debt or business debt. Most often, personal debt is on something like a home or car, wedding w/e so there really aren't any returns (unless ofc you sell your car or home but then you dont have a car or home, do you?).
Imagine I own a business and I get a loan. Now, I'm going to use that loan to maximize my future profits aren't I? I mean, a business can borrow $1 million and pay it back NP assuming they dont go out of business, right? So it's a pretty safe bet - basic economic principles say that I, as the business owner who is now on the hook for $1mil + interests, am very likely to put that money to work. I end up paying my debt just fine and I gave my business more reach and made it more efficient - increasing my long term profits.
It's the same with government borrowing. The government doesn't look for profits, but GDP growth. It's basically the same principle though, they borrow $1 billion and build a bunch of roads and bridges, etc. They aren't just borrowing money and hitting up the local 7-11 for 3 million candy bars - they're investing in the future (LOL totally unintentional Obama reference). By building a bridge that shortens everyones morning commute, those people then save on gas and other expenses (it's small but think about how many people cross bridges every day... it adds up!) and they spend that money on domestic goods instead(remember, we are a service economy) . Workers are more mobile because of highways and roads, which is a good thing for GDP growth as well. The whole point is to maximize long term growth and minimize short term shocks (both booms and busts!).