I feel like the author is overthinking the issue here. People, in general, do not like to be corrected by other people, especially strangers, and see it mostly as the corrector being condescending or trying to show off how morally/intellectually superior they are.

I can agree with that but I think you make a good point here:

...imagine how much more butthurt people would be when your correction of whatever behavior they're engaged in attacks the very core of how they see themselves, that they're a shitty person who's more like Hitler than MLK.

The situation, I think, is distinct enough to warrant specific attention that is beyond an acceptance of people merely being annoyed at correction. That absolutely plays a role but the nature of the correction concerns their personal identity, and one that they're not used to having to defend or even made explicit/relevant in a discussion, and so they get defensive.

I work in IT support, and I always feel like I have to say stuff like "you should probably do this" or "I wouldn't do that if I were you" because as soon as they pick up the slightest insinuation that what they did is wrong, that's when the defensiveness starts to pop up. "If what I did is wrong, then that's means I'm stupid. And I can't be stupid because I'm not stupid." And if there's one thing that will make people flip even more than insinuating that they're stupid, it's insinuating that they're a bad person.

This is partly why I feel that this issue is different (and maybe the author agrees) because I think the problem of "being corrected" largely comes down to things like how you approach them, the language you use, the attitude you take, etc, whereas with things like race issues, I feel like the problem isn't how you dress it up because no matter how you present it, they reject the very notion of things like them being privileged or society needing to change.

So with your IT example, it's like their computer is on fire and no matter what words you choose or approach you take, they are just absolutely insulted at the suggestion that the billowing smoke from the monitor and melting keyboard could be described as the computer being on fire and refuse to accept that something needs to be done.