While proving that you're "right" is often rewarded in academic settings, direct confrontation often leads people to dig into their positions, making it difficult to find resolution or compromise. Your goal should be to get people to move beyond the disagreement, not that you're the "winner." To do that, you need to keep egos in check and give people opportunities to change their minds without feeling like they were "wrong." Productive disagreements should feel like a process of coming to a better collective understanding.
This requires finesse. Try your best to keep arguments impersonal and ask rhetorical questions that lead people to your desired conclusion. Ideally, they'll feel like them came up with the idea themselves (which they have!). By being willing to give them credit for coming up with the idea, you're more likely to get your desired outcome.