"Gonna be hard to win that using a slightly more advanced version of our ilani eight-year-old chemistry.  What with Keltham just destroying the entire country if it starts a war, using the actually dangerous knowledge that real ilani have.  The way, you know, Keltham said under truthspell that he would."

Departing in the middle of the argument may mean you can feel like you won, because the other person doesn't get to fire back at you.  It doesn't actually stop somebody from articulating the real counterargument after you've left and can't argue back.

"Gonna be hard to win that using a slightly more advanced version of our ilani eight-year-old chemistry.  What with Keltham just destroying the entire country if it starts a war, using the actually dangerous knowledge that real ilani have.  The way, you know, Keltham said under truthspell that he would.  You may forget that fact because it's not convenient to you, but I guarantee the Queen and Grand High Priestess think about it very regularly."

Departing in the middle of the argument may mean you can feel like you won, because the other person doesn't get to fire back at you.  It doesn't actually stop somebody from articulating the real counterargument in front of an audience, after you've left and can't argue back.