The most important thing to remember about apologies is their purpose. They aren’t really a time to explain or excuse. They aren’t a time to try to gain forgiveness or get favor. They’re especially not a time to bring up things other people have done.
An apology’s only purpose is to make it clear that you both understand what you did wrong and announce a responsibility for those actions and the damage done by them.
You can express regret and remorse too but ultimately the most important thing is that you’re responsible for what you’ve done and for doing better.
That’s what an apology is for.