At least in the UK (the States may be different), you are taught many of the concepts and underlying reasoning that the author bemoans not having learned.
At A-Level standard, you are taught the physical basis of epigenetic modification (what he describes as switching genes on or off - although that in itself is a too-binary simplification, it's more to do with up- and down-regulation of expression). You're also taught other fascinating processes such as alternative splicing - where a single gene can express many different proteins.
During my first year of undergrad at a so-so Russell Group university, the history of biology featured prominently in lectures - especially those on the evolution of genetics as a field. The inherent fuzziness of categories and concepts in biology was also made very clear. I distinctly remember a lecturer telling us (in response to a question about why we say bacteria don't have membrane-bound organelles, when the topic of the lecture - the magnetosome - was clearly an exception to this rule) that when we say something is 'always true' in biology, we mean it happens 80%+ of the time, and when we say something 'never happens' in biology, we really mean that it happens less than 20% of the time.
I do agree that there is sometimes a bit too much of an emphasis on rote learning the chemical minutiae at the expense of the broader, more important concepts (Krebs cycle, anyone?) - but I think this case is overblown by the author.