I'd add that this kind of misunderstanding is frequently mutual; it's generally not the case that one party is sensitive to tone and the other is immune. The version in which someone takes an expression of feeling as an attempt to shame them into silence or otherwise limit allowable discourse is more or less the same failure mode.

Perhaps I say something, unaware that someone with different experiences and perspective might hear it differently, and it makes you mildly uncomfortable (somewhat like your examples). You try to communicate what you're feeling, perhaps intending only to provide me with more detailed information about the kind of reaction I'm provoking and why (some version of the Emotions As Inputs To Rationality approach). There may be good reasons for your reaction: for example, maybe you've heard things like that before from people who caused related harms, and you want to make sure I'm not likely to hurt anyone or normalize harmful behavior in others.

But then I take your expression of feeling as an anti-rational rhetorical move meant to silence me, because that's a thing that some people do using the same language that you used. Then my following plea for dispassionate rationality and a return to the details of the argument gets heard as dismissive/disrespectful and nitpicking, because, well, you know. And so on back and forth.

(It's also, importantly, not always the case that these are mere misunderstandings. Even if I didn't mean something a certain way, you can still be right that it was harmful to say or that it's a sign that I might cause harm. And even if you're not trying to silence me, it could conceivably be the case that by expressing your feelings you weakened our discourse, although I'm not sure I've ever seen that happen.)