"Apologising means that you value your relationship more than your ego"

There is a popular quote that "Apologizing does not always mean that you are wrong and the other person is right. It just means that you value your relationship more than your ego".

Even if you don't believe that 'piety requires us to honor truth above our friends', or more particularly that the very fact that you have a relationship with the person means you have a duty to tell her the truth, there are less rarefied reasons to disagree with this piece of advice.

If you apologise just to protect a relationship, it means that your apology is devalued (and by extention, and that your other apologies are devalued), and people won't know whether your apologies are genuine or whether you're apologising in order to make the other party feel good.

On a more practical level, not apologising might lead to better outcomes; the other party might realise that she is wrong, or be led to reflect on the situation. Even if this is not the case, one can at least rest assured that one was not complicit in condoning the error: "I have done all I can. The rest is up to you".

So, perhaps, not apologising means that you value the other person more than your relationship.