It's not necessarily about "useful" information, but more about turning enough basic information into knowledge and thinking skills for the child to elicit an interest in the subject or thought process at hand. My high school physics class was enormous fun an I learned quite a bit which laid a foundation for my college physics classes. Not that high school prepared me to pass a college physics test, but rather gave me some underlying principles to which I could refer in class with an, "oh yeah, I remember how this works" notion.
Same with chemistry to chemistry, Earth science to atmosphere and geology, social studies to Western civilization, and so on. High school offers a number of electives which may more interest students and put them on a path toward their college degree. But then again, I know of a large number of students, myself included, whose major wound up not reflecting their high school elective curriculum because we changed our minds or found we were more interested in one subject and less in another than we originally thought.
I wanted to be a fireman. Then a train engineer. Then I thought I'd do computer programming. Even though all of those are great interests of mine (I like to write programs that set trains on fire,) I am instead a criminologist who finds that those boring Western civilization and similar classes had some useful information for me. Oh, as did chemistry and physics for the investigative aspect.
I didn't excel at all of my classes, even the ones I found interesting. Sometimes I excelled at classes I didn't like. In any case, at the end of the day I remember a ton of stuff to which I have been exposed and it makes me a more rounded person with better heuristic and critical thinking abilities. Or, if you prefer, I already possessed these innate abilities and the material to which I was exposed helped to better develop them. Much like playing sports did not for me but did for others.
Had I only taken classes in subjects which interested me, there's a likelihood that I wouldn't be where I am today. I feel pretty lucky as I know several older adults who are only now getting exposed to materials in which they truly excel versus a previous career in which they had moderate interests and lack-luster productivity as a result. (I must also admit a tinge of jealousy toward some of the electives offered to kids in high school today: SharePoint administration and design, Cisco networking, network administration, network security, CSS in web design, database management, and the like. Some of these kids graduate high school ready to pass CCNA and MCSE exams.)
As much as our public school system is being shredded by pervasive bureaucracy and unending political intrusion, it still is one of the best venues for a wide-breadth of exposure to subjects and at least semi-competent people to foster learning of those subjects.
The author addresses a number of my points above, rather dismisses them off-hand with exaggerated examples, with the end result of turning high school into "speed dating" for education. High school is four years, grades nine through 12, with each year offering six to seven classes depending upon the school, for a total of 24 to 28 classes. If you consider a baseline each year of a science, English (reading and writing,) and math, that leaves 12 to 16 classes available. These classes may then be used for self-discovery and other requirements, such as two years of a second language, two years of social studies, two years of civics and history, etc. Not to mention the availability of "dual enrollment" allowing advanced students to enroll in college classes while still in high school.
He speaks of "opportunity costs" of one choice over another, but at the same time fails to address what may lead to those decisions. In his example of selling tomatoes versus cucumbers, consider if said grocer chose to only learn about and ultimately sell tomatoes because he was attracted to the red color, dismissing the opportunity to learn about cucumbers. If said grocer was exposed to all manner of vegetable during his coming of age, he may well have learned to overcome the surface attractiveness of tomatoes and instead chosen cucumbers.
To his specific abhorrence for chemistry: Sure, I don't know off the top of my head how many elements are in the periodic table (I remember around 108 when I was in school and I am certain there are more today) but thanks to chemistry I know that some metals are poisonous, some gases are inert while others are reactive, some gases are deadly and can be given off by innocently mixing cleaning products, that oxygen is required for fire, amongst other things. Can I balance a dual-substitution reaction or do so in my daily life? Certainly not readily, but that does not make the overall course any less valuable to me.
To his apparent admiration of vast stores of information on the Internet, having a reference around is great and handy, but knowing where to find information is no replacement for having knowledge immediately on-hand. Looking up how many elements are in the period chart on Google is a great thing for trivial information, but knowing what it means and how to use that information is knowledge.
This notwithstanding, many students during high school are still learning about themselves and unable to make a number of decisions which will have long-term effect. The more we as parents and educators abdicate our responsibility to parent and educate, and instead attribute long-term decisions which are above the level of experience, knowledge, and maturity of our children, the more we open them and our society up to failure rather than success. Eliminating a base-line of educational requirements and basic skills is the foundation of a societal monoculture which births little to no innovation nor progress.