The author then goes on to provide 6 semi-abstract reasons as to why abstract reasoning matters. Since this question is most likely to be asked by a child, it is code for "how can math-skills make me money or get me a job." Upon hearing the author's answers, 13 year old me would conclude, "it doesn't, and math is as useless as writing poetry". A child who isn't thinking in this practical way is already academic minded and doesn't need an answer. "When will I ever use this?". It obvious! "In next year's math class".
It is sad that a student can leave high-school with almost no classes that ever makes math less abstract. The most beautiful moment in my life was my freshman college physics class. It first filled me with joy and then resent. Because I almost didn't go to college and there was no reason I wouldn't have understood this course at 13. Same goes for finance.
So answers should focus on applications like modeling simple Newtonian physics of a satellite in orbit or predicting the RPM when a 4-stroke engine red-lines based on max-stress specs. Or show them useful short cuts like the Rule of 72 and if they are curious show a derivation. Show examples of ratios/percentages, how fractals can simulate a landscape, ray tracing, or examples of the Fibonacci series in nature, etc.
I find it sadder that many can get through high school without any classes that make it more abstract. Too much of it is just mindless repetition of seemingly-useless incantations that have no meaning or apparent purpose (especially if the concepts aren't understood). Where there are word problems, many students are confused and hate them because they haven't really learned how the math abstracts the situation. (Or how to look at a situation and recognize "Hey, I could abstract this with math to get more information!")
I once tutored a student who hated math and after 11th grade was still failing pre-algebra and wouldn't be able to graduate. After a few months, we had covered algebra 1 and 2, geometry and trigonometry, and a brief intro to calculus and statistics. She aced the test, graduated, and went on to become a successful professional in a job that routinely used math. By then she loved it. Problem? It had never been about the joy of discovering new ideas and new ways to use them. It had always just been shuffling numbers around without any concepts or thought processes that could lead to understanding.
My answers are simple:
Why should you learn it? As with learning to read/speak/write, it gives you another way to think and communicate, and exposure to concepts, some of which you may never use, others of which may someday be very valuable. Even if you don't use them everyday, just knowing that they exist and could be helpful (and recognizing when) is valuable.
When will you use this? You may not personally sit around calculating statistics and probability, but as a manager you may recognize that they could help you make important decisions, avoid problems, and increase profits. So you know to hire someone who can do the calculations, and you have a general idea of what to ask them for and how to understand the reports they give you. And to ask questions to get them to explain the business meaning of things affected by confidence levels or standard deviation so you can understand how that affects your decisions. You'll use it to increase knowledge, success, and profit.
"Education is what remains after one has forgotten what one has learned..." - Albert Einstein