OP, regarding the "secret"... my DP is amazing at connecting with people, defusing conflicts, and just getting people to calm down. He says stuff that I would never dream of saying but it never comes across as condescending. It comes across as warm, genuine, and concerned.
I am not like this. Not very good at connecting, not very good at listening.
I asked him recently about what he is thinking when he talks to people and he says that... everyone is a mirror. When people talk to you, it's not really about you. When someone says somethign to you about you, it's really about them. So you listen to hear what they are saying about themselves.
Then he says that he tries to understand what the other person is saying, about themselves, about the situation, or the conversation, and then when he thinks he hears it, he repeats it back to them to make sure that he does get it. He says he tries to be a mirror. The other person might say, "No, that's not what I meant." Or they might say, "Yes, you understand me."
He says when people hear him mirroring their thoughts back to them that is the only time when he can introduce his own thought. Because now everyone is on the same page. I've noticed people are more willing to listen to him once this happens - and he is in a better position to frame his thoughts in a way that makes sense to them.
It seems like his own intuitive approach to what Naomi Aldort describes in some of her writings as empathetic communication.
Try it the next time someone expresses a harmless opinion that is foreign to you - just echo back the person's opinion to see if you've really understood - and see what happens. I've actually been trying to do this ("Oh it sounds like you don't really like peanut butter chocolate chip cookies, and you're disappointed that no one wants to make the regular chip ones.") and while it feels a little weird to me, I have to say, it works. I've actually had people say, "Now it sounds like you understand me."
It is easier for me to do than offer sympathy, because I feel like I never know what the other person is feeling. You aren't trying to name their feelings or anything like that. (Like, "ooh, that sounds hard." can be met with, "Actually it's not hard...." or "You're angry" with "No, I'm not angry...." unless they actually say, "I am angry.")