How does the Greek example fit your reasoning? Isn't national debt simply collectivized debt? Whether one says that debt is public or private is really academic because the same people possess the debt liability, don't they?
I truly fail to grasp the distinction.
Perhaps there is a limit to debt that is considered optimal and which does the things you explain. I don't know what that is. For me, knowing that there are households and employees where I work who's homes are up for sheriff's sale and who are declaring personal bankruptcy is reason enough for me to manage my debt and even eliminate it.
I cannot understand how my possessing 1 million dollars is the same as my owing someone 1 million dollars.
It's not. It's the same as someone owing you 1 million dollars.
If nobody owes anyone anything, then nobody has any money.
The government borrowing a million dollars is the same thing as the government creating a million dollars.
If the government stops borrowing, then thare is that much less money in existence.
Less money means the money that exists is worth more - the process whereby money gets more valuable over time is called deflation, and it is bad because it discourages investment - why take a risk to increase your wealth, when you can get the same result by just holding on to your cash?
The optimum total amount of money (ie the sum of private debt plus public debt) should ideally in theory be whatever amount is sufficient to produce zero real inflation - that is inflation equal to the rate of growth, which implies zero inflation in real terms. For psychological reasons, it turns out that it is very bad indeed if this falls below zero, so the target inflation rate should be a bit more than that; a little inflation is a good thing, because it stops people from wanting to keep their money in their mattresses, and encourages them to invest it instead.
A lot of inflation is not so good either; so it's all about balance. Right now, lots of people like you are paying off debt. So the total amount of money that exists is falling. But the amount of stuff being traded isn't falling as fast (and we would prefer it didn't fall at all) - so to keep money at about the same value (avoid deflation), someone needs to borrow, to make up for all the people who are paying off debt, and keep total debt (and therefore total money supply) close to what it was.
Right now, most economies need a bit of inflation, to get the guys with the cash to invest it in stuff and get things moving. The way to achieve that in a controlled way is to have someone borrow some money - and if the private sector won't do it, the government must.
The difference with government is that it is in control of its own income - the taxpayers don't get to choose not to buy.