They gave up because of general lack of opportunity.

Possibly a different example can shine some light on the matter. Imagine getting a group of people who are over 30 and do not have a significant other. Then say, "Those people who have not gone on a date in the last 4 weeks are not single because they don't want to have someone in their lives".

Imagine a telling a group of obese people "Those people who have not gone on a diet in the last 4 weeks are not overweight because they don't want to be slim".

"Anyone who has not had an address in 4 weeks is not homeless because they do not desire a home".

You can probably imagine hundreds more scenarios. When faced with repeated failure, many people fail to act in their own interests. In fact, I don't think the unemployment number is necessarily dumb -- it measures the number of unemployed people who have not given up hope of working. But we really need a measure of all the people who have given up hope, but still want to work.

What's unfortunate is the attitude that your question implies (and I'm not actually suggesting that you have this attitude, though it is very common): it is easy to think that people who have given up want the failure that they now experience. Normally this is not the case.

I once saw a homeless person trying to explain to someone their predicament. I don't remember their exact words, but it was something like this: "It's -5 degrees C today. I live in a cardboard box on the side walk. Do you really think that I wouldn't rather sleep in a warm bed? But I've got a lot of problems and this is the best that I can do right now." Followed by considerable profanity (probably their case would have been easier to follow for the listener had that been omitted).

hmm. I thought it worked like this "Persons are classified as unemployed if they do not have a job, have actively looked for work in the prior 4 weeks, and are currently available for work." [1] and "Discouraged workers are a subset of persons marginally attached to the labor force. The marginally attached are those persons not in the labor force who want and are available for work, and who have looked for a job sometime in the prior 12 months, but were not counted as unemployed because they had not searched for work in the 4 weeks preceding the survey."

I don't think it's connected to insurance benefits. I think the statistic is dumb, because it should count people who are available to work but aren't.

On the other hand, if you aren't looking, maybe you really aren't available.

[1] http://www.bls.gov/cps/lfcharacteristics.htm#unemp

I thought that was only the M3 numbers (which are broadcasted as official) while the M6 numbers show the entire unemployment picture?

Of course, I doubt both show underemployment.