anonymouse

But isn't that the point? They don't think that they did something wrong. They didn't intend to hurt you with their action, which they try to convey to you, but they don't think that their action was wrong in principle. Like baking an apple pie for a group where someone is allergic to apples and they didn't know that or simply just forgot. The action of baking a pie is not something to apologize for even if someone felt left out because they couln't eat it and therefore were hurt.

edit (sent the answer too fast)

and they insist that you don’t feel the way you are feeling

okay, I'd say that that is another problem than not wanting for apologizing for one's actions.

It’s that I feel a certain way, and they want me to feel differently without apologizing for it.

I don't think that most people want the other person to feel differently but to make them understand that they didn't hurt them on purpose (that's why they empathize the 'but I didn't mean to') but then they get defensive when they are asked to apologize because to them that means that the offended person thinks that they did do it on purpose, that they did it to spite/hurt them. Like unknowingly bringing up a sensitive topic during a conversation. They don't want to apologize that they spoke about this topic because they don't think that it's a inherently 'wrong' topic to talk about. They do, however, want to convey that they didn't know that this is a sensitive topic to you and they wouldn't have brought it up if they'd known better. At least that's the way I see it if I'm in the position of a neutral observer in this kind of situation.

If your counterpart is actively trying to manipulating you that's different of course but I didn't interpret the comic from that point of view.

Exactly. I'd interpret "I'm sorry you feel this way" passive-aggressive as well and that's the reason I wouldn't want to push someone to apologize to me if they don't want to. How do THEY get to apologize for MY feelings?

I guess it's just a difficult situation to be in. I think it is okay if you do something another person doesn't like/hurts them but not apologize for it. You didn't know it better. If they tell you that they were hurt by your action then acknowledge it ("It wasn't my intention. I won't do it again.") AND DON'T DO IT AGAIN (if it's a reasonable request and/or you know the person)! Simple as that. People don't HAVE TO apologize for their actions especially if it's something that isn't offensive to most people and they couldn't have known someone else doesn't like it. Of course it would be nice to hear "I'm sorry I hurt you" or something along those lines too, but I also understand that they don't want to apologize if they don't see a problem in the act itself. But If they still proceed to do the action then I'd be pissed (again if it's a reasonable request).

What would it help if they apologize if they don't mean it/see what they did wrong? If it wasn't person As intention to hurt person B, but B insists that person A apologizes, it would result in A apologizing for Bs feelings aka "I'm sorry you feel this way". I don't think that that's better.