If the labor force participation rate was still at 66% or higher as it was for 82 out of 96 months that Bush was President, the unemployment rate for December 2014 would be 10.33% instead of 5.6%. A labor force participation rate of only 62.7% makes a huge difference when compared with 66%. Your talking about roughly 8 to 10 million people.
You realize that all you're saying is "If more people were unemployed, then the unemployment rate would be higher."
But why did you choose 66%? The LFPR started dropping in 2000. The reason it's been dropping is that a larger percent of the population does not want a job.
But here's some fun....If we had the same labor force participation rate as Lyndon Johnson, then the unemployment rate would be negative (I can provide the math if you'd like). That a negative result is possible shows that the whole methodology is bogus.
It is clear to me that the poster chose an LPR of 66% because that was what it was for 82 of the 96 months that Bush was in office. The question you should have asked is why does a larger percentage of the population not want a job?
Let's look:
Arbitrarily choosing December 2006 (a year before the recession, the Population was 230,108,000, and the labor force was 152,571,000 for a rate of 66.3% (all numbers will be not seasonally adjusted). 13.1% of the population was 65 or older and not in the labor force. In December 2014, it was 14.7% So right there that's 1.6% lower LFPR.
Those not in the labor force and enrolled in school went from 5.2% to 5.8%.
Unfortunately, data on those with disabilities only goes back to 2008, but since that number has clearly been going up since then, that's another push.
And there's no way to measure stay at home parents as timely, but from the 2006 average to the 2012 average the number of one earner families went up.
I'm not sure why you think it matters why people don't want a job, though.