Monetary union came from the desire to achieve a united Europe one where constant conflict would be minimised. But the process was not thought out carefully or if it was the problems were ignored.
Greece was the 10th member to join the EEC in 1982 the UK was the 8th or 9th. This shows the significance the European leaders attributed to Greek entry. There were vast political reasons as to why Greece was hurried through and before Portugal and Spain. Those reasons are still there and have nothing to do with the fact that Greece is a major contributor to the economic well being of the continent. It has a strategic importance and that significance remains the same today, so alienating the country is not a good idea as the Greeks might look to Russia or China for help.
The solution to the problem is a difficult one and it will involved giving Greece more space to repay its debts to the bankers in Berlin and London otherwise the anger felt by the people will torpedo the euro project. But saying that I am not sure the euro can be saved given that Spain is one street away from collapse and if this or when this happens a bail out will not be possible so the European leaders are taking the piss out of all of us, they know the euro is dead.