Yes you do have an obligation as a member of the human race to appologize for accidently upsetting a fellow human. Just because you didn't intend to cause pain does not mean that their feelings are less painfull. Talking about 9/11 is perfectly legit. Upsetting someone who lost a loved one and not appologizing for accidently causing the pain would be a dick move. Compassion and empathy are extreamly important parts of human interaction. The internet forgets that far too often.
So if I started talking about ham sandwhiches and someone started crying (for whatever reason - maybe their family was eaten by savage pigs), I would be obligated to apologize? Or let's say someone become upset becaus my shirt bore a certain shade of red(maybe they were red-green colorblind and my shirt reminded them of their disability), I would also be obligated to apologize? That's the argument you're making with the bolded. Using your argument, you would be apologizing 15, 20 times minimum per day as people are bound to be upset by your words (unless you don't talk much). You would have to apologize to people with the craziest, most vulnerable sensitive topics. Is that how you live your life?
I would guess the answer to that question would be no. You don't go around apologizing to every sensitive person out there just because they are the ones who easily become upset. No, you probably create a spectrum in your mind containing when you are obligated to apologize for something and when you aren't. On one end of the spectrum lies things you probably wouldn't feel obligated to apologize for regardless of who becomes upset (though you may do so anyway to ease the feelings) - like apologizing for wearing a red shirt. On the other end of the spectrums lies things you are more likely to feel obligated to apologize for sense it's more understandable for someone to become upset by it - like accidentally driving over someone's pet cat. In this particularly case, yes, it would be a dick move to just casually continue your day after killing someone's pet.
I agree that apologizing would be the compassionate move and one that helps ease the tension, but there's nothing morally wrong about it.
Good job coming up with the most absurd situations possible. But I will say that if someone was as emotionally unstable as to cry over the color of my shirt I think I would probably apologize and put on a jacket to keep from upsetting a clearly disturbed individual that deserves even more compassion that a emotional stable person.
I don't know what world you live in where you meet people who burst into tears over every word you say. You either know a lot more people with emotional problems than I do your you go around saying mean things to everyone you see.
I haven't made anyone cry in a very long time, even by accident. I can't even remember the last time. But I have apologized for making someone visibly uncomfortable due to the discussed topic. I apologized, changed the subject and things were pleasant again.
Exercising compassionate isn't just a tool to get out of a tense situation. Be compassionate is part of having empathy. You know, that thing in the back of your mind that makes you identify with other humans. It's that that thing that without it we would be a savage race of thugs.
If you make someone upset you are supposed to feel bad about it because you identify with how you would feel if someone upset you. It's not even a question of morality. It's part of the human condition. Nobody should go around actively trying to hurt other people's feelings. Some do, that's why we have words like "jerk" to describe those who don't have compassion.