My initial response was to go "Hey man.... I didn't know it was. And because of that, you shouldn't take it offensively because that wasn't the intent." I tried to twist it around like I was the one being picked on (without really realizing it). When the reality was,
all I needed to do was say "Oops, I didn't realize" and stop doing it. Because if someone says "Hey man, I find the term you're using unpleasant" I have a decision to make: "Do I want to continue using this word knowing it makes someone feel unpleasant?" If so, why?
Because if your motivation is "because I want to keep using that word because I think it's the best word for it" you're saying "it's more important to me to be able to use that word to describe you than how that word makes you feel." In some cases it's maybe appropriate (i.e. referring to someone that committed a murder as a murderer), but in the case of sexuality or race, I am less insistent on using words because I feel the reasoning behind doing so is rather selfish and unnecessary.
Unless I perceive a consensus among trans people that they are cool with the term "it," I see no reason to use it if people tell me that they find the term uncomfortable. Nor do I feel that I can tell them that they shouldn't feel uncomfortable by it because that's just my privilege... I don't have the experience and negative connotations associated with it. It's why I stopped using the term "gay" when I meant something is absurd.
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.
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.
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