I've been thinking about this as a general pattern, and have specifically filled in "you should be thick skinned" to make it concrete. Here's a thought that applies to this concrete example that doesn't necessarily apply to the general pattern.
There's all sorts of reasons why someone might feel hurt, put-off, or upset about how someone gives them feedback or disagrees with them. One of these ways can be something like, "From past experience I've learned that someone how uses XYZ language or ABC tone of voice is saying what they said to try and be mean to me, and they will probably try to hurt and bully me in the future."
If you are the rationalist in this situation, you're annoyed that someone thinks you're a bully. You aren't a bully! And it sure would suck if they convinced other people that you were a bully. So you tell them that, duh, you aren't trying to be mean that this is just how you talk, and that they should trust you.
If your the person being told to change, you start to get even more worried (after all, this is exactly what you piece of shit older brother would do to you), this person is telling to trust that they aren't a bully when you have no reason to, and you're worried they're going to turn the bystanders against you.
Hmmmm, after writing this out the problem seems much harder to deal with than I first thought.
In light of reading through Raemon's shortform feed, I'm making my own. Here will be smaller ideas that are on my mind.