Usage of "I'm sorry" and "thank you very much" outside of obvious settings

Why do people say "I'm sorry" at the beginning of a sentence? For example: "I'm sorry, but I don't care for her one bit." On the same note, I would like to understand the meaning of "thank you very much" at the end of a sentence, thus: "I said I'll take it to go, thank you very much!"

Any light shed will be greatly appreciated.

There are quite a few intended meanings of these qualifiers; here are some examples of possible meanings of "I'm sorry," with each interpretation in parentheses.

"I'm sorry, can you tell me where the library is?" (Excuse me...)

"I'm sorry, but that doesn't work for me." (I hate to have to tell you this...)

"I'm sorry, but no." (No matter what you say...)

"I'm sorry, what did you say?" (I beg your pardon...)

"I'm sorry, I just couldn't get there on time." (I have a good excuse if you want to know...)

"I'm sorry, I said vanilla, not chocolate." (Were you paying attention...?)

"I'm sorry, I totally screwed up." (Please forgive me...)

"I'm sorry, but she went to jail?" (I can't believe what you're saying...)

"I'm sorry, I'm busy right now." (Stop bothering me...)

"I'm sorry, I tried to stop him." (It's really not my fault...)

I could come up with even more, but I hope I've made the point that English is tremendously flexible, and that context, inflection, intonation, the situation, and the demeanor of the speaker, all influence meaning to the point that the same two words can mean dozens of different things.

English has many such stock phrases used to qualify disagreement or disapproval:

• I'm sorry, but....
• I'm sorry you feel that....
• With all due respect, ....
• Don't get me wrong, but....
• In my humble opinion, ....

They can express an honest desire to soften the impact of a controversial statement, but they often indicate thinly-veiled hostility or insubordination. For example, Wikipedia cautions its editors not to use “With all due respect”:

When addressing another editor, it is normally better not to start with the phrase “With all due respect” as everybody knows it really means “Go [screw] yourself.”

In spoken English, these phrases sometimes carry a sarcastic tone to indicate overt hostility. That's likely the case in “I said I'll take it to go, thankyouverymuch.”