I don't mean to be counter to the popular grain, but if it wasn't your intent to be offensive, and someone decided to be offended at the word, then they kinda did decide to pick on you. I don't know what their reaction was after you made your case, but if it was to continue to act indignitive or possibly to become more antagonistic, then I would say they were in the wrong, regardless of what word you used.
Their reaction was "then why do you feel compelled to continue using the word?"
I didn't really have a good answer. Years later, I feel I felt defensive because I knew being a racist was a bad thing, and if I admitted to using a racist slur then my personal self image now has to reconcile the question: "If I acknowledge that I used a racist slur... does that make me a racist?" Which is a terrifying thing to face because I knew being a racist was wrong and I didn't believe I was a racist. The brain (which I do not believe we have full control over) is exceptionally good at rationalizing things to eliminate cognitive dissonance, and it's a major amount of cognitive dissonance to try to reconcile the idea that I performed an action that I would typically classify as only being done by racist people - a status I didn't want to believe I could be.
And while I do agree with your reasoning, about whether something is worth using simply because of preference or not and that them letting you know something was offensive did offer you a choice, I can't really see someone being offended as a good enough excuse for someone to get their way all the time because, well, being offended is pretty much a meaningless statement of emotion. Given your example, I can see why the situation might be a bit hard, it was a derogative name used during WWII, which was the period you were discussing in, and its history is quite bad. But by that same token, the person who is offended also has a choice, on of how they react to someone being offended and the expectations involved. Now, I am hoping this person who brought up being offended did the right thing and was understanding to your misunderstanding, not trying to make you feel bad and allowed bygones to be bygones. What I really hope they didn't do was demand you not just stop but also apologies, and then lorded your misunderstanding over you like it was some kind of scarlet letter.
I suppose they have the choice to not feel offended. The thing is, if this is true, then I have the choice to not be bothered if their reaction is anything more than allowing bygones to be bygones. If they can choose to not be bothered by that, I can choose to not be bothered by them demanding apologies, and I can choose to not be bothered by them "lording my misunderstanding over me like it was some kind of scarlet letter."
Because to me, it seems the bulk of your point is immediately solved by practicing what you suggest the other person should do. The thing is, it always seems to be the "other person" that has to do something. At the time I was defensive. But now, I can look at it and say to myself "I was in the wrong. All the other person did was tell me that it was a racist slur and they would appreciate that I stopped doing it." Even if they said "Hey *******, that's a racist slur" it doesn't really change the fact that I used a racist slur.
If you and I (and I mean literally, you and me) are talking and I say something that bothers you, then it's up to me to evaluate whether or not it's worth me continuing to use that phrase. If I respect you as a person, I better have a good reason to keep using the word. If my original usage of the word was "I didn't know any better" then if I insist on keeping using it despite you telling me that it's offensive, then it may in fact be that I don't respect you all that much after all.
Context and understanding is important though. If you tell me that you find the use of the word "the" offensive, you'll need to elaborate on your reasoning as to why. It's not like someone is just saying "I find the word 'it' offensive." They've substantiated why (They find it dehumanizing). It's a position I can understand. No one is saying that they find the word offensive without substantiating why, in this case.
And to try and illustrate my point, I will now quote a famous person whose outlook on this matter matches my own.
“It's now very common to hear people say, 'I'm rather offended by that.' As if that gives them certain rights. It's actually nothing more... than a whine. 'I find that offensive.' It has no meaning; it has no purpose; it has no reason to be respected as a phrase. 'I am offended by that.' Well, so ****** what." - Stephen Fry
I feel Stephen Fry's quote is misused a lot. His quote is specifically with regards to a law that would prevent negative commentary to "stir up religious hatred." It's important to note that Fry's views don't really align with organized religion. They use it as a general position "no one can claim to feel offended" and to rationalize continuing to act like a jerk.
It first comes up in an article by The Guardian. It should be noted that Fry takes offense to things like homophobia, antisemitism, and racism. Like most people, he probably is disinclined to validate "I am offended by that" for people that espouse morals and values that are not in alignment with his own.
I don't know what his response to insisting on referring to a trans person as "it" would be (someone could ask on twitter I suppose), but I actually wouldn't be surprised if he felt that someone insisting on using the term was a dolt.