Why did the students of Abu Hanifa, Imam Ahmad, and Malik contradict their imams?

The disagreement of the companions of the imams with their imams is one of their greatest virtues, because they investigate what the texts indicate and follow what the proofs from the Book and the Sunnah establish. The imams enjoined their followers to prioritize the Book and the Sunnah over their own statements. Thus, the companions' disagreement with the imams in some minor issues is a form of obedience to them in prioritizing the text. Imam Al-Shafi'i recounted the consensus that whoever has a clear understanding of the Sunnah is not permitted to abandon it for the statement of anyone. The four imams explicitly stated that their words should not be given precedence over the words of the Messenger of Allah, peace and blessings be upon him.

Abu Hanifa said: "If I say something and the Book of Allah contradicts it, then abandon my saying for the Book of Allah... And if the narration of the Messenger of Allah, peace and blessings be upon him, contradicts it, then abandon my saying for the narration of the Messenger of Allah, peace and blessings be upon him... And if the saying of the Companions contradicts it, then abandon my saying for the saying of the Companions."

Al-Shafi'i said: "If I say something and there is a contrary [narration] from the Prophet, peace and blessings be upon him, then what is authentically narrated from the Messenger of Allah, peace and blessings be upon him, is more worthy, so do not imitate me." He also said: "If an authentic narration contradicts my madhhab, then follow it and know that it is my madhhab."

Ahmad said: "Do not imitate me, nor imitate Malik, nor Al-Thawri, nor Al-Awza'i; rather, take from where they took."

This confirms that what was mentioned in the question about the companions of the imams disagreeing [with them] is among their greatest merits and the merits of the imams themselves.