Algebra is the underpinning of symbolic logic.

You can argue that analytic geometry teaches a somewhat limited form of deduction, but, no, you can't reasonably say that algebra teaches logic. Like all math, it's just a way to describe quantities and the very limited relationships between them.

Unlike the author, I do think algebra and geometry are a useful part of an education, which, unlike the author, I think should have nothing at all to do with job training.

If we really want our kids to learn to think, then we're going to have to actually give classes on thought: induction, deduction, abduction, analogical reasoning, dialectical reasoning, and causal reasoning. We're also going to have to give them the information and ideas they need to reason with: history, literature, philosophy, and social studies. Finally, we'll need to ensure that they can express their thoughts: rhetoric, composition, and basic math.

If we really want to educate, instead of just train, we're going to have to make room for a real education, and that means clearing out both shop and calculus. Just like auto mechanics, most higher maths are only useful for very particular jobs, and as such they're just job training, which employers should be doing, not education, which is what schools should be doing.