How to debate without quarrels?

Nowadays, it’s like that. They call it an echo chamber. We just listen to our own point of view and then keep giving replies without hearing out others. Often when people argue, they set up a strawman, knock it down and say they won the argument. In classical Hindu debates you have to restate to that other person's satisfaction before allowed to reply.

You can see how many quarrels it would prevent. Most of the time when we argue, it degenerates into quarrels because we’re not really listening to what the other is saying.
We think of a reply that is going to blow away the opponent without trying to understnd what they really mean.

In ancient Indian debates, if you say something, before I reply, I must restate to you what you said to your satisfaction.

"Is this what you said?"
"Do you agree?"
"If you yes, then, I can reply."

"What is non-dualism saying?"

"They are saying this..."

"Is this what you said?"

And we say, "yes".

Ah, now we listen.

And, then he proceeds to shred non-dualism to pieces.

When Ramanujacharya attacked advaita vedanta in the classical style, he restates the position of advaita vedanta. In his book, Mahapurvapaksha, "The Great Opponent" (non-dualists), Ramanuja gives a very fair re-statement of advaita vedanta. One of our Swamis who's a great scholar and a very staunch non-dualist admits that Ramanuja is a gentleman because he does a fair job of stating our position.