Flip this mindset around. Think about how many times words have hurt women in the past. (I’ll go by your definition here so, no, not me or other transwomen.) People saying women shouldn’t have rights is harmful, yes? People saying lesbians are sinful and disgusting or something is harmful, yes?
I know this is completely different from what you’re trying to say, but the whole “Words dont hurt” argument, in my opinion, has a lot of room to backfire. Theres so many scenarios where words do hurt people, and if you flip this around to anyone else, does it sound pleasant or nice? No. It sounds like being a dick.
Say you switched this around to the verbally abused, who were degraded and hurt over and over by guess what? Words! Say you switched this around to women. Say you switched this around to the LGB (Excluding trans because again, not talking about trans people here yet.) community. It would sound incredibly wrong.
So now is the point most people would ask, “So why do this to transwomen!?” buuut, that isn’t the point here. I’m a transwoman, but I also grew up with well, constant abuse. I’m not getting into it, I don’t want to, but point is, a lot of that was verbal.
Theres transwomen who have been degraded their entire lives, not even for being trans, just for being a person. So yes, I understand this doesnt correlate with what you’re saying, but words can hurt anyone. It doesnt matter if you’re cis, trans, gay, straight, white, or a PoC, words CAN hurt you. Words can hurt anyone, getting upset shouldn’t be a sign of privilege, unless it’s over your spilled cheerios, or some other stupid concept.
You cannot run around and degrade a group of people, no matter what type, and not expect ridicule in return. I kinda rambled here, but that is all.