"but" expresses conflict, nuances and compromises. Life is not simple and our thoughts, actions and feelings are often not rational or in line with each other, there for dismissing anything before "but" is a way of actively not listening.
- "I believe in free speech, but some opinion are too abhorrent to be protected." -> Maybe free speech should not allow people to slander, extort, abuse people? Or at least not give them a jail free card.
- "I am sorry I reacted like this, but they went too far" -> This person can indeed feel sorry and feel somewhat justified, because maybe both parties involved did something worth being sorry for.
By the look of it, what this reply is saying is how point 7 describes the negating qualities of "but", while the point immediately following it uses the said word.
> Anything you say before the word “but” does not count.
> When you forgive others, they may not notice, but you will heal. Forgiveness is not something we do for others; it is a gift to ourselves.