Hyuga Yu's reason for killing the three spies was simple: he wanted Aburame Ryūma to see it.
Within Root, a system even more ninja-like than the ninja themselves, anyone who wanted to seize greater authority had to demonstrate correspondingly greater "value."
Whether it was the authority to assign Might Duy, whose combat strength was "under observation," his own future path of training, or using Root as a towering tree to fend off the Hyuga Main Family and the powerful figures from various nations who were clearly about to come arrest him—
Hyuga Yu needed to gain more say within Root!
But clearly, Hyuga Yu had misjudged Root as it currently stood.
Root's use of the Hyuga Main Family as bait, the far-from-accidental "misassignment" of Might Duy, along with the mysterious "Kirigakure Collapse Plan" mentioned by Aburame Ryūma and Kirigakure's future collapse...
All of these things had caused Hyuga Yu to overestimate Root's strength.
But in truth, once that deliberately manufactured "strength" was stripped away, Root's role in the Third Shinobi World War was essentially nothing more than one of Konoha's intelligence agencies.
Aburame Ryūma was one of that agency's foremost spies. His absence meant that there was currently a mission only he could carry out—and had to carry out.
And the ability explicitly listed as his greatest specialty in the databook was infiltration.
At this time and in this place, the only place worth Aburame Ryūma infiltrating was Kirigakure itself, sealed off by the Bloody Mist.
In other words, At this very moment, The "Kirigakure Collapse Plan" Aburame Ryūma had mentioned had already begun!
Hyuga Yu could not judge the full scope of that plan, but with even Root's second-in-command dispatched on a mission, Root's remaining forces on the Kirigakure front were far weaker than he had imagined. Root's grasp