Franklin also describes a technique whereby you don't directly tell someone they're wrong, you simply tell them that in this particular case the circumstances are different.
E.g., the bad way to do it:
Person A: "We should do X!"
Franklin: "You are wrong. We should do Y!"
E.g., the better way to do it:
Person A: "We should do X!"
Franklin: "You are, of course, right that X would work if P and Q were the case, but here R is the situation. Don't you then agree that Y would work better here?"
This way, your "opponent" gets to preserve the feeling of being right, or at least avoids the defensiveness that follows being told you're wrong.
Yes, the trouble is that such exchanges are often a battle of egos on both sides. Person A has an egoic need to be right, and Person B has an egoic need to prove person A wrong and themselves right.
No doubt this is an effective technique, you just have to be able to release your own ego and also not directly challenge that of the other person.
I think the point is that this approach is meant to reduce the effect of ego and allow the other person an easier way to change their position.
All public differences of opinion involve ego, status and other emotional states. It's a case of finding a way to lessen their effect on all parties (oneself included).
E.g., the bad way to do it:
Person A: "We should do X!"
Franklin: "You are wrong. We should do Y!"
E.g., the better way to do it:
Person A: "We should do X!"
Franklin: "You are, of course, right that X would work if P and Q were the case, but here R is the situation. Don't you then agree that Y would work better here?"
This way, your "opponent" gets to preserve the feeling of being right, or at least avoids the defensiveness that follows being told you're wrong.