The "sound argument" of the title refers to the cold logic that sacrificing one individual (Historia) is a necessary evil to save the nation.
The episode concludes with the realization that while the plan was logically "sound," it destroyed the very humanity the Survey Corps fought to protect. Attack on Titan - Season 4 Episode 10 - "A Sound Argument"
: In the present day, we see the tragic outcome. Historia is shown pregnant and despondent, seemingly having accepted a fate she never wanted. 10 : A Sound Argument
: The episode highlights the growing instability of Eren, who has grown cold and detached, alarming his closest friends, Mikasa and Armin.
Set two years before the present-day conflict, the episode explores the introduction of foreign diplomacy to Paradis Island and the tragic weight placed on Queen Historia. The Visit from Hizuru The "sound argument" of the title refers to
: A small-scale display of the Wall Titans' power to deter world invasion.
: To maintain the Founding Titan's power, Historia must inherit the Beast Titan and produce as many children as possible during her remaining 13 years. The Emotional Rift Historia is shown pregnant and despondent, seemingly having
: In a poignant flashback, Eren Jaeger vehemently refuses to let Historia be used as a "breeding tool".