> I genuinely don't understand the intensity with which you and others respond with.
I'll try to explain. I think it's a very strange request to make, especially to people you aren't close to like random co-workers. Imposing on others can put them in an uncomfortable position. It would be easier for them to say "No, if you choose to feel excluded by an explicitly and objectively inclusive phrase with full knowledge that it isn't being used with any intention to exclude you, that's 100% a 'you' problem. Please handle your shit and don't make your problem into everyone else's problem.", but most people probably won't want to be rude, so many will just agree. Depending on the power dynamic in play, some people may feel that they have little choice at all, or that the consequences of non-compliance could be career limiting.
For you the whole interaction is the request, followed by their response, followed by your judgement, but for the polite others it involves making an active effort to be conscious of every moment where you're within earshot, remembering the common and innocuous phrase that upsets you for some strange reason, and then actively changing the way they'd normally express themselves to others in order to accommodate you. In addition to having to constantly remember to self-censor, it also means risking feeling like shit if they happen to slip up, or worse, worrying about the impacts their mistake might have on their career or the work.
It's absolutely not the most demanding demand you could place on another person, but it isn't nothing either, and when the reasons for that demand don't make a lot of sense, having to actively make and continuously maintain that effort can feel like a larger imposition than it might otherwise, especially in a busy environment where there's work to be done and people's heads are already filled with other concerns.
A request like that could easily be seen as rude, self-centered, or off-putting in a professional environment even when the same request made to your friends and family would likely be better received. Being able to clearly explain why you have the issue you do in a relatable way might help avoid some of those negative feelings. If it isn't a deliberate choice on your part to twist other people's innocently spoken words by willfully ignoring the very definition of them and turning them into something that makes you feel bad inside, and you find that even if you try you can't help but feel that way about it, in all sincerity, I'd recommend finding and speaking with a therapist about it.