1. Advising is teaching. In fact, advising is the majority component of an R1 teaching load! So, he DID discuss the teaching component of his job. A lot.
2. In terms of classroom teaching, he was probably teaching 1-2 courses per year at Harvard. So classroom teaching really wasn't the majority component of his job. It's unsurprising that he didn't spend much time talking about this minority component of his job, in the same way that it's unsurprising when a developer talks primarily about writing/reading/testing code rather than the ~20% of their workday activities that are something other than writing/reading/testing code.
Of course, one hopes that developers introspect on their effectiveness in various meetings, when talking to clients or internal stakeholders, and so on. But you'd be unsurprised if a dev, discussing their biggest mistakes during their first few years, focus on code-related mistakes.
3. Maybe he felt good about his non-advising, classroom teaching? The title of the post is "everything I did wrong", not "a summary of everything I did".