It is very simple really, and the author dealt with it in his article.
If we look at the 2 largest currency unions in the world (excluding the Euro).
The Dollar works because of federal intervention. The successful states are forced to send vast amounts of money, via the federal government, to the unsuccessful states. For example, despite New York having 3 of the largest 5 non-federal debts in the US (New York City, New York State and the Metropolitan Transport Authority are all in the top 5 borrowers list), New York still has a massive economy, so it is forced to send money to poor states in the Mid-West or South in order to flatten out the economy. This is no different to the South East of the UK massively subsidising the rest of the country.
The African French Franc works simply by being tied to a much larger economy (the Eurozone now, and the French Franc before that). For this to work though you need orders of magnitude difference.
The Euro has none of these mechanisms. To a certain extent it started working for the periphery economies simply because they were tied to a much bigger economy (franco-german centre). Unfortunately, as they got access to huge euro lending markets at very low interest rates, the economies became much bigger, without the substance behind them to support them. They are now no longer small compared to France or Germany (especially when you look at Portugal, Ireland, or even Spain, Italy. They could mirror the USD by Germany, France and the other northern economies flooding money south, but that won't wash politically. We are stuck with some pretty miserable other options. Even the writing off 50-70% of the debt of Greece option that the author talks about won't really help because Greece is in Primary Deficit - it cannot pay its way even if it defaults. The usual way countries deal with this is the combination of 3 things. Austerity, default and devaluation. The Eurozone is trying to force Greece to deal with it using only austerity. That is doomed to failure, and to be honest, even if we let them deal with it using default as well, it is probably too late. The only way to devalue though is to leave the Eurozone.
If I were a betting man I would say there is as much as a 50% chance that Greece falls out of the Eurozone. This is not dissimilar to the UK falling out of the ERM, and the funny thing is economically, that was really good for Britain!