Why is the EUR/USD pair still going up?
This chart shows the exact reason, and why it will probably continue.
It's because of the widening spread between the yields on 10-Year German Bunds and 10-Year US Treasuries.
10-year government bonds are the most highly traded and liquid debt instruments for a sovereign nation. When the yield on these securities rises, it means that investors are expecting higher inflation or higher growth in the future (during economic expansions).
When the yield on German Bunds started moving up faster than the yield on similar US Treasuries in March, that's when the FX market started to react by exhibiting higher prices for EUR/USD. This is because inflation in the EuroZone is rising quite fast, while in the US it is still stagnant. This is leading investors to bet on higher growth in the EuroZone relative to the US.
The yield German Bunds right now doesn't seem to show any sign of stopping, so as long as they keep going up, the Euro may go right along with it.