I think that has several causes:
1) Greek politicians (and Greek elites complicit with them) consumed a lot of infrastructure money from EU in BS overpriced public works projects. That said, Greece infrastructure wise is a totally different country from Greece in 1980. But those infrastructure projects didn't and could't themselves generate money.
2) Greek economy was traditionally based on smaller production units (SMEs). When global outsourcing (and later China and co) became an option for everything of that kind, Greece competence in the area dropped to 0. The small business owners at the time didn't have the savvy to market their products as premium goods and justify higher margins (like e.g. Italy does at least for some things), neither did they have the brand name to assist them in moving production abroad (and continue selling). The quality+price points they competed at were no longer possible. Tons of such Greek industries died off in the 80s and 90s with no replacement.
(Add to the mix a bevy of EU policies that were in fact protecting interests of major EU nations (Germany, France, mostly), against competition from the South).
3) Even so, Greece had control over its debt, which was never a major part of GDP before 2001, using its monetary policy. The inflection point was the switch to the Euro, when suddenly a volatile economy was tied to a "strong" currency, with no room for corrections (imagine the US debt if the Fed couldn't print dollars and the world didn't accept dollars as a de facto exchange currency -- now imagine that with an much weaker economy to begin with).
