This is because its monetary policy and its independence could be compromised. The risks taken by the Eurosystem must therefore be limited to what is required by monetary policy and by the goal of ensuring the transmission of the monetary policy to all parts of the euro area. There are very good reasons for not monetizing budget deficits in countries with a national currency.
There are even more reasons for not doing so in a monetary union such as the euro area. Before the crisis, it was too often argued that current account positions between members of a currency union are meaningless, and that there cannot be balance-of-payments crises within a currency union. The last couple of years have proven the fallacy of this view.