Let's take a moment to change perspective:

Imagine you worked for years on something and finally uploaded it on ArXiv, waiting for the community to weigh in. The following characters appear:

1. Someone known in the field does not bother reading it but says you are probably wrong, bets money on you being wrong and says he does not want to be bothered with it. How would you feel?

2. Someone else known in the community starts collating information/comments to help verify the proof or find instructive mistakes.

3. Another mathematician also believes Blum is wrong just because it is statistically likely, and does not want to spend time on something that will most likely lead nowhere. She keeps this opinion to herself and simply does not engage with the material. If approached, she declines to comment because she says he did not have time to check the proof.

Aaronson went for option 1 and in my highly personal opinion, it's the worst of the ones listed. It's standing at the sidelines being snarky. Just because he may as well be right does not make this behaviour any better.

It is the equivalent of laughing in an undergrad lecture when someone asks a naive question.

I just want the problem with his behavior to be accurately diagnosed, because I think (again, I could be wrong) the solution is "better manage your temper with your non-academia fans" and not "rethink your relationship with other academics".

Sounds like most academic paper reviews!

I have no personal familiarity with this specific instance, but your assessment is likely correct. "Putting out the fire with gasoline" is pretty common on the internet. I have seen celebrities on Twitter reply to something they did not like, only to be surprised and grumpy that their attempts to shut it down backfired and just resulted in more of the thing they did not want, plus additional collateral damage of various sorts.