The winner will use logical points of his argument while his opponent will use emotional appeals that do not hold any logical weight.
One of the best examples of this is from the conclusion Star Trek TNG's episode "The Drumhead" where Captain Picard is being charged with being a traitor to the Federation (for defending a crew member who was by any objective measure in the wrong place at the wrong time) by a much respected Admiral Sati (who is the daughter of the widely respected late Judge Sati, who is so influential in the whole of the Federation, many of his rulings are required reading for anyone in Picard's line of work). At the tribunal, being observed by the Admiral in charge of security in Starfleet.
Sati presents damaging evidence to Picard's character which Picard acknowledges is true (and from previous episode, but with an unfavorable light cast). Picard offers in his testimony a summation of the situation that Admiral Sati's investigation has evolved into by his famous "With the First Link" speech, which in universe is a quote from one of Judge Satie's rulings:
"You know, there are some words I've known since I was a schoolboy. 'With the first link, the chain is forged. The first speech censured, the first thought forbidden, the first freedom denied, chains us all irrevocably.' Those words were uttered by Judge Aaron Satie as wisdom and warning. The first time any man's freedom is trodden on, we're all damaged."
Upon hearing these words, Admiral Sati condemns Picard for having the gall to invoke her father's words to justify his "betrayal" but its implied through her emotional response that she is appalled at using her father against her, rather than any fallacious read of Picard's interpretation. The Admiral who will be deciding the outcome of the hearing promptly gets up and silently leaves the room as Sati continues her rant and it is only when he is out the door does she realize she had lost the case and is left to silently think over what happened as the entire assembled court audience, including her own support staff, leave her in silence.
In this scene, Picard's quote is from a work that is the fundemental belief of the Federation, that should the freedoms and protections it grants not be afforded for even the most seemingly guilty member of a society, it will be done so anyone else. Picard's crime is defending a man accused of a crime and for that he himself is labled a traitor. And when Picard moves to defend his own actions, he invokes defense of what is commonly understood bedrock truth of his society's fundamental philosophical principals. Whether or not you agree with the quote, Picard had already stated it's original speaker was so correct in his logic that they had to require Starfleet Officers to read those judgements before becoming even a junior officer. When Sati's response is to demand that an accused traitor is not allowed to speak of such an accepted assesment of his own rights and that traitors who do sully the speaker, the room is forced to conclude that Picard has a better grasp of Sati's stalwart defense of principals than his own flesh and blood. Picard, and the attendence of the hearing admired Judge Sati for the words he spoke, but Admiral Sati, his daughter, showed that she only admired the words because of who it was who spoke them. She betrayed her father in the eyes of the Federation because to her, the words lost all value when a less honorable man spoke them and she was willing to call for more betrayal of the ideas they carried.
This demonstrates another important matter in debates, is that some time it is more admired to stick with principals when it is inconvenient rather than abandon it when it asks us to do things we do not care to do. Remember that Picard is defending a person who did lie about his family relationship: his grandfather is a supposed immigrant from a nation that is now in a cold war state with the Federation and the crewman hid that fact to get to his position. Because of this, the crewman is under intense investigation by Sati for possible espionage (which is not grounded in hard evidence) and Sati is moving the possible into realm of accepted fact without even a trial. It is not easy for Picard to afford defense to a man who is guilty of the small lie and the big lie never confirmed (the viewer is left to decide if the crewman did or did not). The small lie is enough to likely end the crewman's career, let alone the accusations not yet proven. Defending him is not to Picard's benefit and if he never did, no one would blame him. Certainly not Sati. It serves no benefit for Picard to hold to his conviction and do what's right while doing what is wrong will keep him out of the eyes of suspicion. All Picard has to do is compromise on his principal and yield that the quotes of the a dead judge were not really important to his career and his duty to his crew. As another Starfleet Captain in another situation once said, all it would cost is "The Self-Respect of one Star Fleet Officer" and Picard... Picard could not learn to live with it.