Part of this is an intentional misrepresentation of the employment numbers. In order to be counted as "unemployed" you must first have had stable "employment". Thus, people just out of high school or college that are unable to find their first job (which is often extremely hard to come by) are not counted as unemployed, despite being so. The other problem is that after unemployment benefits expire, people aren't counted as unemployed anymore, so the unemployment stat goes down, but the percentage not in the labor force goes up.
Employment indicators U3/U6 are remarkably poor for depicting gainful employment in the wake of economic depressions; they're meant to measure unemployment that is expected to be transient. Super long-term unemployment, difficulty finding a first job, and underemployment are not adequately measured, though the part-time employment stat is somewhat taken into account.