German and British politicians and IMF officials are fond of talking to the Greeks as if they were doing them a favour by offering any debt write down or bail out at all, even on the extreme austerity terms they're offering - and that Greeks can take it or leave it.
The dominant view seems to be that Germany and other northern EU members were doing Greece a favour by letting it into the EU and the Euro-zone, or that Greece is so backward or corrupt that it should never have been allowed in to either. This is very far from the truth. In fact Germany gains massive amounts of trade income as a result of weaker economies' membership of the Euro.
Greek membership of the EU and the Euro-zone has actually boosted German exports to Greece and to the rest of the world massively - and if Greece leaves the Euro German exports both to Greece and to countries outside the EU will fall and so German export earnings will fall.
With Euro currency zone membership the first reason is that before the Euro was introduced as a common currency the German Deutschmark was worth many Greek drachma. This meant that German exports were too expensive for most Greeks to buy, so they would be more likely to buy cheaper products made by Greek or other producers or companies. With the introduction of the Euro the price of German exports was effectively lowered, so Greeks bought more German products, increasing German exports and export earnings.
The second reason is that the value of the Euro is based on the average economic strength of the entire Euro-zone, making it worth less than the Deutschmark, which had a value based on the very strong German economy. As a result, with the introduction of the Euro, German exports to countries outside the EU also became cheaper to buy for consumers in other countries - once again leading to an increase in German exports and export earnings.
If Greece leaves the Euro the crisis will likely spread to, at the least, Portugal and Spain - and possibly to Ireland and Italy, meaning all those countries might leave the Euro. They would then return to their own, weaker, currencies, effectively increasing the price of German exports to buyers in those countries and reducing German exports.
On top of that each weaker economy leaving the Euro will increase the value of the Euro, meaning exports from Germany and any other remaining Euro-zone countries worldwide will rise in price to buyers in other countries, reducing exports for Germany and any other remaining Euro-zone countries.
With EU membership the reason is free trade between a relatively strong developed economy and a barely developed one. German and British and French industries and companies built up over centuries of protection and subsidy before World War Two and decades of investment (including the lion's share of Marshall Plan aid) after it, are free to export to Greece and Portugal and Spain with no barriers up to protect Greek or Portugese or Spanish industries and companies or allow them to develop.
The Graph at the top of the page is from Antonio Fatas' post on Insead blog