I'm not saying i have the answer to this, but i also worry about damaging the relationship in those cases. so i instinctively end up trying to validate something about the other's words, their situation, their values, the thought process which led then to their initial argument, or anything else i can think of. something like

• "but i can totally understand how someone would feel that way (their initial position) considering (reasons)"
• or "but what do i know, I've never (had certain relevant experience)"

if I'm honest i feel super awkward doing so after having argued/debated against their side. and I'm always afraid they'll call me out as a hypocrite, a pedantic simp, or just a plain idiot who doesn't pay attention to my own words....

and much of the time, the other person ignores my effort. at least that's no worse than if i didn't say anything extra.

but sometimes, their expression will change from confused/irritated to relieved. or they'll confirm that they were convinced by me and don't resent what I've said. so it can work.