Behind the hope that computers can replace teachers is the idea that the student' s understanding of the subject being taught consists in knowing facts and rules, the job of a teacher being to make the facts and rules explicit and convey them to the student, either by practice drills or by coaching. If that were indeed the way the mind works, the teacher could transfer facts and rules to the computer, which would replace the teacher as drillmaster and coach. But since understanding does not consist merely of knowing facts and rules, but of the grasp of the general concepts underlying them, the hope that the computer will eventually replace the teacher is fundamentally misguided.
The statement 'It is possible to program computers so that they can teach the understanding of general concepts that underlie specific facts and rules' would most seriously undermine the author's conclusion that computers will not eventually be able to replace teachers.