Seems some kind of misunderstanding or manipulation take place.
Eurozone easing is a good sign for eur, while usd easing is a good sign for ... eur.
We have got the same monetary easing, no matter under what sauce, but both is good for eur and bad for usd, even if one is from ecb and other from fed. Very fundamental view. I suspect that eur overbought, but someone seems broke the button sell and now can press only buy one.