We should first examine Nichiren Daishonin's intent in inscribing the Gohonzon. Regarding one he inscribed for the family of the believer Shijo Kingo, he states in "Reply to Kyo'o":
The lion, king of beasts, is said to advance three steps, then gather himself to spring, unleashing the same power whether he traps a tiny ant or attacks a fierce animal. In inscribing this Gohonzon for her protection, Nichiren is equal to the lion king. This is what the sutra means by "the power of an attacking lion." (mw-I, 119)
Through this passage, we can sense the intensity and depth with which Nichiren Daishonin poured his heart and soul into inscribing a Gohonzon for the family. Such profound compassion for his believers is vibrantly apparent in each of his letters.
In contrast, however, as is clarified in the answer to question 3 in this pamphlet, Nikken's behavior runs completely counter to the intent and compassion of Nichiren Daishonin. Instead, Nikken has been a driving force behind attempts to destroy the SGI's kosen-rufu movement for people's happiness. In terms of his state of life, Nikken has become the least qualified person to act on behalf of Nichiren Daishonin in transcribing the Gohonzon.
It is quite natural, then, that many members, in reaction to Nikken's conduct, have chosen to exchange the Gohonzon he transcribed for one transcribed by the twenty-sixth high priest, Nichikan, who struggled to restore the Daishonin's spirit and intent within the priesthood during the eighteenth century after it had been compromised by previous high priests.
On one level, we can state that any properly transcribed Gohonzon embodies the life of Nichiren Daishonin, and Nikken's transcription of the Gohonzon is technically correct. Yet knowing now that Nikken's intent and behavior are at complete odds with the profound compassion of the Daishonin himself, many have opted to receive the Gohonzon transcribed by Nichikan. This way they can chant to the Gohonzon without being reminded of Nikken's misdeeds.
An additional motivation for some exists in the fact, detailed in a previous answer, that the teaching Nikken is trying to dissemminate about the Gohonzon - that he personally empowers the Gohonzon, and that only through his sanction can one derive benefit from chanting to it - is a clear perversion and slander of the Daishonin's teachings.
By chanting to the Gohonzon transcribed by Nichikan and showing benefit and actual proof as a result, many feel they are refuting both this erroneous claim as well as Nikken's false contention that the Gohonzon of Nichikan is counterfeit. Buddhism teaches that refuting what is erroneous and unjust in terms of the Buddhist Law is a profoundly good cause. Since the Gohonzon is the essential crystallization of that Law, this may in part explain the tremendous joy and progress reported by many who have exchanged Gohonzon.
A Pamphlet Published by the Soka Gakkai International-USA, 1997.