Defeat the Purpose of an Apology by Adding 'BUT'
I have had someone apologize to me on more than one occasion and this person has consistently added 'but you hurt me' or 'but you made me mad' to the end of their apologies.
To me this completely negates the apology and what I hear is "I'm sorry that you're to blame for my actions and I am only apologizing because you think you I should and not because I mean it."
'But' added to the end of an apology will cause the receiver to feel that you are insincere and are just trying to further wound them.
If you are hurt by something someone said or did and you are sorry for what you've done, make the hurt element part of a different communication, and give the other person time to have your apology sink in first. Many times that person will see what they've done and realize that you got hurt as well.
And, because they feel your apology is sincere they themselves will often look at their part and apologize for their actions.
Give them time to see their error and try to fix it after your apology and you might not have to bring up how you were hurt too because they will.
Bottom line leave out the 'but' and avoid the temptation to tell them they need to say their sorry while you are apologizing.
Like they say... an apology is about THEIR hurt feelings and not YOUR hurt feelings.
I have still never felt that this person was really sorry for anything because of the big 'but' added to their apology attempts and it seems that many others react to this kind of apology the same way that I did, and still do.