He is being a jerk. Also, not responding to the actual argument, as far as I can tell (which is technical, but quite clear). There are some other damning statements in the rebuttal, too--for example, they say that all the new machinery developed for anabelian geometry lies unused in the case to which Corollary 3.12 applies (meaning most of the effort mathematicians have been spending in order to try to understand Mochizuki's new mathematics has been wasted). They also mention other incidental complexities that serve to obfuscate the argument but don't seem to buy anything (for example, not choosing a specific isomorphism at one point in the proof, but instead asking the reader to consider all isomorphisms with particular properties, for reasons he has been unable to justify). Someone in his position should be aiming to clean up his proofs to be as straightforward as possible, not making them deliberately harder to verify.

This is typical behavior in Japan when you question someones authority. It doesn't go well with them, it's a direct attack on their honor. You really need to go deeper with him (over dinner or so), but he refuses, so most likely he is wrong snd he knows it.

If nothing else, this new criticism can be used to clarify and improve the original proof. This response is .. not encouraging.

Math academic community is actually very healthy overall, in my experience.

see: monty hall problem

But anyway, mathematics is not any more unhealthy than any other field, but it does have toxicity like all others do as well.

My understanding is that the Monty Hall problem was just a cute puzzle published in a pop-sci magazine that confused a few professors who perhaps ought not to have been confused by it. I don't think it says anything at all about the health of the mathematical community.

It was also ambiguously worded, which is the bane of probability problems posed by people who think they are clever (like vos Savant).

I will repeat what I wrote about this point a couple of weeks ago: According to vos Savant, in most of the cases where the correspondent actually had a correction to offer for her alleged error, they were assuming the intended interpretation of the puzzle.

Your understanding of the history of the problem is lacking and you've caused me to get downvoted as a result, thanks for that. The professors were misogynistic towards her as they could not believe a woman could solve this problem. She even addressed this.

Given the anecdotal correlation between math and autism, and the effects of autism on sociability, one might expect mathematics to have different toxicity.

I never went deep enough into mathematical academia to judge, let alone getting into other fields to allow for a comparison.

Well, let's lay aside the fact that there clearly are plenty of jerks in academia. The entire article seems to layout a sort of string of unusual and problematic situations. Whether it's people who hit upon the problem conjecture and chose not to speak out for fear of causing trouble, or the journal publishing the proof being edited by the author, or the large number of 'delegates' who seem to be pushing the proof without being able to explain the proof, it seems this is a mix of problems that are arising from an unhealthy situation.

If the objections really were founded on a basic misunderstanding, then one would expect a straightforward clarification to be forthcoming (where 'straightforward' should be read in the context of the formidable mathematical abilities of the parties to this dispute.) Its absence suggests that this is bluster (though that interpretation is made through the filter of my western/English-speaking cultural background.)