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"I convinced you to commit suicide."
"No you didn't! I convinced you to commit suicide."
I'm quite aware that some systems make combat in non-physical spheres so mechanically parallel to regular physical combat that the same sorts of consequences are available. What I am saying is that this sort of conflict bears no relation to any of the social interactions we commonly experience, to the point that they would seem supernatural or magical or alien.
Well, yes, if you are doing it wrong.

Let us remember - being Taken Out in FATE is being reduced to a defenseless state, so that your opponent can do what they want to you, including rendering your character permanently unplayable. One possible form of unplayable is death, but it is not the only form. But let's take death as the example.
For a social conflict, it shouldn't be, "convinced you to commit suicide". It might be more like, "I have so thoroughly ravaged your reputation such that everywhere you go you are met with scorn, derision, and bullying, so that you eventually succumb to depression and commit suicide." But even then, you'd want to avoid narrating it as stipulating the character's actions. So, "so damaged your reputation that there is no succor anywhere, and everyone views you as a target. In short order you are worn down to the point where you get a dagger in the back in a dark alley, and die," is more appropriate.
But, the more real case is probably, "I have so damaged your reputation that your landlord throws you out. Your employer now thinks you are a child molester and fires you. The bank won't loan you money. Your friends slam door in your face and won't even let you crash on the couch. The cops think you are scum, and find every excuse to drag you in to try to pin crimes upon you. You can no longer survive in the society of this town, and have to move away. Please make a new character."
None of these are supernatural, or even particularly surprising. My first example happens to teenagers bullied on social media with alarming regularity.
Social conflict that normally bears the stakes of death is not something anyone normally experiences and certainly nothing that just spontaneously happens because someone chooses to socially attack someone. It's a disassociated mechanic.
Not at all. It isn't like someone walks up to you, call you names, and you drop dead. Just as a physical attack must happen in a fight scene, the social attack must happen in a social arena, a place where social ties and bonds can be damaged. If done properly, it is no more dissociated than physical combat is, as the resulting narrative makes perfect sense in context.
In most social interaction we experience the risk is basically only "how various statements are perceived".
Apples to apples, please. Most physical interactions we experience don't run the risk of death either. Thus, we don't use the *combat* system for them. You probably don't use combat to adjudicate a game of ultimate Frisbee, or an arm-wrestling match. You use the combat system not for "interaction" but for deep and serious conflicts where broken bones, lacerations, and death are intended results.
Social interaction is not social *conflict*. Social conflict is where someone is using social positioning to bring real harm upon another.