So ... I honestly think this is a problematic reply ... I think you're being defensive (and consequently maybe illogical), and, honestly, that would be the red flag I'd look for to indicate that there's something rotten in academia. Otherwise, there might be a bit of a disconnect here ... thoughts:

• The calculator was in reference to arithmetic and other basic operations and calculations using them ... not higher level (or actual) mathematics. I think that was pretty clear and I don't think there's any "fallacy" here, like at all.
• The value of learning (actual) mathematics is pretty obvious I'd say ... and was pretty much stated in my post about alternatives to emphasise. On which, getting back to my essential point ... how would one best learn and be assessed on their ability to construct proofs in mathematics? Are timed open book exams (and studying in preparation for them) really the best we've got!?
• Still forgetting with open book exams ... seems like an obvious outcome as the in-exam materials de-emphasise memory ... they probably never knew the things you claim they forget in the first place. Why, because the exam only requires the students to be able to regurgitate in the exam, which is the essential problem, and for which in-exam materials are a perfect assistant. Really not sure what the relevance of this point is.
• Forgetting after coursework ... how do you know this (genuinely curious)? Even so, course work isn't the great opposite to exams. Under the time crunch of university, they are also often crammed, just not in an examination hall. The alternative forms of education/assessment I'm talking about are much more long-form and exploration and depth focused. The most I've ever remembered from a single semester subject came from when I was allowed to pursue a single project for the whole subject. Also, I didn't mention ordinary general coursework in my post, as, again, it's pretty much the same paradigm of education as exams, just done at home for the most part.
• Rebuilding education toward employer centric training system ... I ... ummm ... never suggested this ... I suggested the opposite ... only things that were far more "academic" than this and were never geared toward "productivity". This is a pretty bad staw man argument for a professor to be making, especially given that it seems constructed to conclude that the academy and higher learning are essential for the future success of the economy (which I don't disagree with or even question in my post).
• You speak about AI a lot. Maybe your whole reply was solely to the whole calculator point I made. This, I think, misses the broader point, which most of my post was dedicated to. That is, this isn't about us now needing to use AI in education (I personally don't buy that at all for probably much of the same reason you'd push back on it). Instead, it's about what it means about our education system that AI can kinda do the thing we're using to assess ourselves ... on which I say, it tells us that the value of assessment system we take pretty seriously ought to be questioned, especially, as I think we both agree on, given the many incredibly valuable things education has to offer the individual and society at large. In my case, I go further and say that the assessment system is and has already detracted from these potential offerings, and that it does not bode well for modern western society that it seems to be leaning into the assessment system rather than expanding its scope.