The last thing they want is the euro to get strong and eat into their fledgling trade surplus and, in general, do its deflationary thing.
But what can they do? Discourage Japan and the rest from buying their member nation’s debt? Not.
Buy $, yen, etc? No- ideologically impossible. Gives the appearance that fx reserves are backing the euro, etc.
That leaves ‘monetary easing’ of some sort that doesn’t directly work, but hopes to scare investors out of euro.