Take the definition that is given by the relevant government agency, which is the BLS's U-3 measure.
(Now you might argue that U-6 is also a valid measure etc etc, but only a Breitbart writer or somebody willfully ignorant would confound unemployment with labour force participation.)
It's completely irrational to exclude "the percentage of people who aren't employed" from the set of possible definitions of "unemployment." Each of the various measures of unemployment captures meaningful information about the economy.
Labor force participation rate lets you look at important trends in the economy. For example, labor force participation went way up when barriers to women entering the work place were removed. Women didn't want to all be stay-at-home moms, but the economy didn't offer them any other opportunities. These days, drastically more of the population is going to post-secondary education, which tends to drive down the labor force participation rate. But that's really a paradoxical phenomenon when you think about it, because at the same time, the costs of such education are skyrocketing. Why do people eat the cost (including the opportunity cost) of going to college? Is it because of the love of learning? No, it's because the economy doesn't offer them alternatives.
Of course you can't count every student or retiree or stay at home mom as unemployed. Many don't want to be working. But it's equally irrational to assume (as the BLS does), that none of them want to be working.
