How can the euro possibly enter an uptrend against the USD?

  • If the risk-off mood continues, it will be because of sovereign debt worries or fiscal tightening. In that case, the euro should fall, since the Eurozone is where both of these dangers are most real.
  • If a risk-on mood returns, the euro is the obvious funding currency for carry trades: rates low for longer, likely down-trend (a reflexive argument). 
What is wrong with this picture?