I am not sure I can be of help to you in this situation.

I think it sometimes helps in these situations to have the reason for an apology clearly in mind. A "clean" apology is one with no ulterior motives; no strings attached. Before one can express this though, one must own it in one's very self. If one wants something for oneself in the apology or even wishes for something, then it is often not the right time to make an apology. I guess what I am saying is that the apology must be 'clean' in one's mind first. That is the really hard part.

It is difficult to not want something in return for something given. And it is easy to fool ourselves in this. It may sound easy but it is actually quite difficult. I don't know of course but I wonder whether the apology you wish to make has a sort of trap door in it, in that you at least wish that the outcome of the apology will be a restoration of the friendship? Am I wrong?

An apology is a kind of gift. And a real gift should not have any strings attached.

If one feels that one has wronged a person, hurt a person; there is a difference between feeling that one is sorry because it has caused one to have a lower image of oneself, there is a difference between this and wishing to offer something to someone who one has hurt.

The first intention is restoring one's self esteem and focuses on the self. The second type of apology is totally focused on the other so the self almost disappears. A good apology is one where one kind of says: I am sorry for what I did to you and I have no further expectations beyond that. That, I think, is a kind of "clean" apology.

Why is this often difficult?

The more one loves oneself, the less one needs to "import" love from others. If one loves oneself say at 99%, one is not that needy and is not really desperate for love. If one is unable to love oneself as a result of childhood experiences and upbringing then one's inner needs are too strong to allow one to really give love. If one loves oneself 10%, and can only love oneself 10% then one can't really spare any love except perhaps needy love. The most one can hope for is often just a relationship of selfishness-for-two.

If you feel you can offer a real, sincere apology, then I would say: go for it. Go for it, but expect nothing in return.

Of course I could be wrong. I am often wrong about things. But that is my fallible opinion.

Best of luck!!!