In one sense the reason we still have unemployment is simple - we never had a classical recovery from the recession, we just had a return to normal growth. If you look at almost any historical recession you'll see a spike in unemployment, a dive into negative GDP growth, and a dive in inflation. Then, during the recovery you'll see a spike in GDP growth, a spike in inflation, and the employment level recovering to what it was pre-crash. This recession didn't have peaks in growth and inflation, just a return to normal. If you just looked at the GDP and inflation charts (or a combined NGDP chart) you'd expect that we'd still be having high but falling unemployment right now.
And I could get into a big, long discussion of why this happened involving IOR, and the Fed relying on indicators that are always months out of date, and zero bounds, and certain coughdallascough Fed regional bank presidents being idiots. But whether or not there are supply side problems contributing to high unemployment in the US now, the demand side indicators show we should be having high unemployment now so there's no need to go "WTF".