Let me tell you something: none of those reasons, or variations thereof, are anywhere near a good enough reason to apologize for what you about to say. Especially as in all cases, you do not mean it.
It really has reached the stage whereby I have now – in person – started picking people up on their use of this phrase the moment it leaves their mouths. Take an exchange with a colleague only last week:
Me: I really don’t think this is a good idea.
Them: I’m sorry, but –
Me: Why are you sorry?
Me: Why are you sorry? You just said “I’m sorry, but…”
Them: Well… (embarrassment) it’s just something you say isn’t it?
I exited the room before they could spout whatever their opinion was, purely and simply because I knew by adding that prefix, it would be completely nonsensical and totally irrelevant. I never did find out what it was they wished to say to me, and I’m glad, because in all honesty, I couldn’t give a shit.
Putting that bloody awful phrase before a statement, whether factual or not DOES NOT give you carte blanche to be an outright bastard and use the fact that you uttered that completely senseless phrase as a get out of jail free card.
It’s fine to have a different opinion, it’s even fine to be a bit of a bastard sometimes. We all do it, and sometimes it is necessary to bring someone up short and make them think about what they are doing. But by apologizing for daring to possess an opinion, you are making yourself look weak and pathetic. Own your actions and opinions. It is entirely fine to be wrong sometimes. Then, if you deem it necessary, you might decide on balance that you were a little unreasonable or unfair or you may indeed recognize you caused someone to be hurt when it genuinely wasn’t your intention and in that situation it is fine to apologize. Go to the person, state your case and why you said what you did and say “I am sorry if I hurt your feelings, I really didn’t want that to happen.”
Say it the right way, not with a nasal, whiny tone laced with a sense of entitlement: “Well, I’m sorry, BUT…”