How can Greece have so many debts?

By having been scammed by the EU.

Corruption and lies. When it first joined the EU, Greece was already in financial difficulty but did not let the EU know just how bad things were. And the corruption continued - people who should have been paying their taxes didn't, and lied about their incomes. Anyone in a government job has little or no worth ethic - I've talked to people who have visited Greece and missed vital travel connections because someone in Greece didn't feel like coming to work that day, and didn't bother calling the office to let anyone know. The shame of it is that ordinary Greeks are caught in the middle of all this, they are the ones to suffer. I would love to know what the PM is telling them to keep his job, because I suspect whatever he's telling them is very different to whatever he's telling the rest of the EU.

As for Greece being scammed, like every other EU member state, it was given money to improve its infrastructure, education, medical care, and other things. The question is where did much of that money go to, whose private swimming pools were funded with it.