In those examples it's the statement that's offensive, not the individual words used to express it. If I'm having an argument with someone and they imply I'm me

In those examples it's the statement that's offensive, not the individual words used to express it. If I'm having an argument with someone and they imply I'm mentally deficient, it doesn't matter what words they use to say that; the statement itself is inherently offensive. Here however it's not the statement people are objecting to (most even seem to agree with that part), but one particular word that was used in expressing that statement. That's a different thing entirely, and it's what I mean here when I talk about a _word_ being offensive.