Arjuna's birth as a supreme warrior, destined for greatness, makes him the ideal pupil for Drona, who secures a promise from him to defeat Drupada as his teacher's fee.

This is a direct causal sequence: Drona's training of the Kurus (specifically the Pandavas) enables them to capture Drupada as his preceptor's fee, which is the central action of the humiliation.

The divine weapons and knowledge Drona obtained from Parashurama are the specific assets he possesses that enable him to demonstrate his skill to the Kuru princes and become their preceptor.

Drona, having become the official preceptor to the Kuru and Pandava princes and having completed their training, is the causal agent who observes their readiness. His role as their teacher is the necessary precondition for him to formally propose the public display of their skills to the king.

Drona's humiliation of Drupada and seizure of half his kingdom (in ss_adi_128) is the specific insult that directly triggers Drupada's plot for revenge, which he executes by seeking a son through sacrifice.

Drupada's long-standing plot for revenge against Drona (ss_adi_128) is the underlying motive for his intense interest in the identity of the swayamvara winners. His desire for Arjuna to marry Draupadi, expressed through the priest, is part of his plan to ally with a powerful enemy of Drona (the Pandavas).