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" 10 : A Sound Argument
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
: In a poignant flashback, Eren Jaeger vehemently refuses to let Historia be used as a "breeding tool". 10 : A Sound Argument