Since I find myself just now having offended a friend by asking too much of a business favor, I am particularly sensitive to this question. My first reaction was to justify how I was right and be offended at her reaction. But upon further consideration...I know her well enough to know I was asking too much, how she would react, so I should have known better. Although I might have responded differently than she did, to be a friend is to accept each other as we are, and I truly value her friendship.
I agree with "msorensson"... Once I got into my heart about it, I honestly explained where I was coming from (not to make myself right and her wrong, but so she could understand my motivation) and then apologized for not being more thoughtful.
What works for me is to find my heart in the matter first, then it comes to me what is natural and authentic to say.