If you want to point to the single concept that has to be re-examined to understand basic income it is this one:
"Paying people to do **nothing** when there
is **so much** to be done seems crazy to me."
It speaks to the foundation question of value for capital that is pounded into our heads (in the US at least) from birth that if you want to make it you need to get a job that pays well. And it forces us to ask the very important questions and re-examine some of our assumptions.
Some of the things I have thought about when considering BI have been, is it really "nothing" we are paying for? Lets say you're living in a neighborhood without any jobs available, and without jobs and property taxes your educational infrastructure is lacking, and without a job in the first place your mobility is lacking. However you do find employment in selling illegal drugs, the market is wide spread, the risk is low for the street level dealers. Now into that market your provide a basic income for the youth who can now pursue their interests without participating in some form of underground economy. Can you see paying people to not participate in that economy?
When I think about BI I have come to think about removing worry rather than paying for 'nothing'. IF you look at income disparity versus economic efficiency, economies grow when there is incentive to get ahead but they begin to contract once that disparity exceeds a threshold. If the bottom of the economy is worried about where they are going to sleep and eat tonight, they aren't very efficient or contributory to the overall GDP, if the top end of the economy is keeping all of its wealth bottled up in trading games with other top end users, it isn't contributing to the overall GDP either.
If you force disparity to zero, you essentially get communism, if you leave disparity unconstrained forever you appear to get monarchistic type trapped wealth. If you change the rules of the game so that people can be wealthy or not, but the total difference between maximum wealth and minimum wealth is constrained to 2 orders of magnitude rather than 4. Perhaps you get a better system overall.