I think the problem could be seasonal adjustments. Seasonal adjustments are based on historical patterns, weighted more heavily towards the recent past. The surge in unemployment last year at this time is used to “seasonally adjust” this month’s figures.
That may be part of it, however not counted as unemployed are those unemployed over 1 year and discouraged (a 'fix' put in under Clinton after he signed NAFTA), or those long term unemployed who are not eligible for extended unemployment because of the timing of when they lost their jobs but are eligible for early SS. Both categories are removed from the civilian labor force.
GOVERNMENT ECONOMIC REPORTS: THINGS YOU'VE SUSPECTED BUT WERE AFRAID TO ASK!
Unemployment as counted in the 1980's is closer to >20%.
Meanwhile per PEW ~8 million illegal aliens have jobs, and 125,000 new legal workers are brought into the US each month.