I'm Sorry.

There's a song that goes, "Sorry seems to be the hardest words." But it's not the words that are difficult. It's meaning them. And not stopping until the injured party believes you do.
-Mitch Albom-

It's not the sorry that people seek, but the knowledge that the person is well and truly, regretful of their actions...

Perhaps when those five letter spouts like a watering can off our flowery society, it seemed more of a polite gesture, than a well meant, sincere apology.

Because when you do it brashly, there's no need to swallow your ego and humble yourself.
And when the other party refuses to accept the apology, or show signs and indications that they are still not letting it go, you became furious and upset claiming that the whole purpose is to make you feel bad.

Is it fair to say that this mindset is in fact, Individualistic?

Saying sorry doesn't put you in the mercy of others. It only puts you within the confrontation of your conscience and yourself. Because you know that you are gripped with a sense of contrition, when you understand the other party might not be able to fully forgive you.

That's when you place yourself in a disposition that allows you to say that you truly are, sorry.