I think politeness could serve a purpose. It might be a placeholder until forgiveness is ready to take its place. There's no hypocrisy in reacting with gracious calm, even when inside we're appalled.
And after that, distance could be useful, too. It could shield us from being provoked more while we process the ugliness that's been shown us thus far. The freeing thing is this: there isn't a deadline for forgiveness. It comes when it comes. If you watch for its approach you'll only end up brooding over the slights and offenses that need forgiving. You can't really keep taking its temperature, checking for the exact moment the fever breaks and you're free of resentment.
You just go about living life and delighting in what's good and eventually something triggers the memory of when you were betrayed or some crappy thing that came out of this person's mouth, but now you can think about it without gritting your teeth or calling the person some choice invective or picturing him or her in various forms of purgatorial suffering.
No, no, when you can recall it all with detachment, like a deathbed review of your own life, that's when you know. And won't you be glad then? You'll be relieved that you carried yourself with dignity, never stooping, never taking the bait. You reined in your expectations, allowing the other person to operate within their current, somewhat limited awareness of humanity, divinity, and magnanimity of spirit. You gave them no deadline to reach your level of consciousness.
You resisted the very tempting impulse to solicit sympathy via the posting of meme after meme of pseudo-wisdom or sarcastic wit that does nothing to veil the vat of stewed bitterness that used to take up space in your heart. Yay you!