“The weak can never forgive, forgiveness is the attribute of the strong” and so is apologizing.
A simple sorry can save a breaking relation.
Often when you cannot let someone go, you rather consider apologizing better than losing someone.
I have done that too, but doing so will eventually erode your relationship anyway.
It shows that only one person is willing to hold on to the relationship and the other person will just take the benefit of the other one’s politeness.
In my opinion, In spite of apologizing without your mistake, try to communicate and decipher the actual issue.

In my case, my boyfriend doesn’t say sorry to me even if it’s his fault.
When i’m at fault, I say sorry to him and give him the assurance that he needs. But when he’s at fault, I only get a ‘goodnight’.