1. Governments can raise taxes.
Governments can compel a large swathe of the population to give it unrequited transfers known as taxes. Households cannot.
2. Governments can print money (at least those that enjoy monetary sovereignty).
Governments can print pieces of paper that will be gladly accepted as payment for goods and services. Households cannot.
Note though that this power is not a widow's cruse. The limiting factor, constraint, or trade-off is inflation. See this discussion: Smith (2014).
3. People die.
There is thus a (literal) deadline at which a person's assets and debts must be resolved. A person cannot remain in debt forever.
In contrast, there is no obvious deadline for governments. A government can be in debt for pretty much forever:
The US has been in debt every year since its founding (TreasuryDirect.gov — the debt came close to zero in 1835–36).
The UK has been in debt every year since at least 1694 (Ellison & Scott, 2017, Fig 1).
Yes, a high and rising debt is undesirable.
However, if say a government consistently maintains a 40% debt-to-GDP ratio for 200 years, then most economists would consider this perfectly healthy and sustainable. In contrast, it is not generally possible for an individual to be in debt to the tune of 40% of her annual income for 200 consecutive years.
4. Governments can borrow at much lower interest rates (thanks to the above factors).
On 2019-01-31, the US government's average interest rate was 2.574%. This is lower than the rate at which most Americans would be able to borrow and certainly much lower than their credit card interest rates.
5. Government budgets directly influence economic growth.
When an individual decides not to buy a new fridge, this does not affect her income. But when government cuts spending, this likely reduces national income, which, by the way, also tends to reduce the government's own income (i.e. tax revenue).
Conversely, when an individual buys a new fridge, this expenditure does not increase her income. One individual's expenditure adds to others' income, but not to her own.
But when government increases spending (on anything other than imports), this does result in increased national income. A country's expenditure is its own income.
When an individual suffers a fall in income, it may be prudent for her to cut back on her expenses. In contrast, when a country suffers a recession, it is not usually prudent for its government to reduce spending.
Every family in America has to balance their budget. Every small business. Should we expect anything less from a great nation? (Jeb Hensarling, 2011.)
The above is a common piece of rhetoric used by pro-balanced-budget politicians. There are two mistakes.
First, as already alluded to above, we have the fallacy of composition: What is true of the parts need not be true of the whole.
Second, the premise is not even true. Many families and businesses do not have balanced budgets and are in debt.
This though is not necessarily a bad thing. An individual in law school, a family that's just bought a home, and a firm that's just built a factory may all be in debt, but we do not ipso facto disapprove of them.
Likewise, if a government spends its money on productive and legitimate uses (and not mostly on fireworks and bridges to nowhere), we should not condemn it simply because it is running a deficit.