There are 2 very different kinds of arguments. Arguments where you're trying to convince the other person. And arguments where you're trying to convince bystanders. These require completely different tactics.
If you're trying to convince the other person, be humble. Be gentle. Be subtle. Ask them questions. Let them think they came up with the idea entirely on their own. If any bystanders are watching this discussion, they are more likely to think that the other person is right, or that they are "winning". But this will give you the best possible chance of convincing the person you're talking to.
If you're trying to convince bystanders, project confidence. Present compelling evidence. Pick apart the other person's arguments and show why its flawed. Chances are, this will make the other person dig in even more strongly and resent you. But this will give you the best chance of convincing neutral bystanders.
Use the right tool for each job. If you're using "debate tactics" in a 1:1 discussion, you will never get the desired results, no matter how data-driven and logical your arguments are. I've made this mistake far too many times, and this seems to be what OP is getting at as well
I like this distinction, but it reminds me to cherish the people who don't require such confidence games.
Feynman has a famous anecdote about sitting around the table with senior scientists in contentious argument where he was perplexed because it was obvious to him who was right. They argued all sides, and ultimately agreed, having proofed the idea and its alternatives.
That's who I want on my team: people who can shake things out without needing to be right or needing others to be humble, and without playing games. After viability, that's my primary criterion for a position.
If you're trying to convince an audience, it matters how you treat the person you're arguing with. Don't be a jerk. People notice that, and judge you for it. They judge your position for it - perhaps not intellectually, but emotionally.
The best possible thing to do in that situation is to out-evidence them, out-argument them, and out-nice them. And really, if the facts are on your side, you shouldn't have to be a jerk or manipulative.