Korah's rebellion was unforgivable because he created disunity among the Jewish people.
The following article is reprinted with permission from the Orthodox Union.
The rebellion of Korach and his followers brings out a side of Moshe Rabbeinu (our teacher) that has not yet been seen. Moshe's role is usually that of caring shepherd and intercessor for Klal Yisrael (congregation of Israel) when they sin. On their journey from Mitzrayim (Egypt) to Eretz Yisrael (land of Israel), Moshe always pleads with Hashem to be understanding and merciful, to forgive the offenses committed against Him.
Now, however, Moshe's attitude seems to change. When Korach questions his authority, Moshe seeks only justice! Why, asks Rabbeinu Bachya (14th-century Spain), does Moshe respond differently than he did by the sin of the golden calf and the sin of the spies, when God's supremacy was challenged?
It is possible that Moshe is more protective of his own honor than of Hashem's?
Undoubtedly, the Jews' faith in Hashem, which should have remained firm after all they had witnessed during the exodus, was sorely lacking during the sin of the golden calf and the sin of the spies. These two sins surely mark two of the lowest moments in our people's collective history.
These situations, orchestrated by Hashem, gave the Jewish people opportunities to succeed and grow. Whether at the shores of Yam Suf (Red Sea), the foot of Sinai, or the border of Israel, Klal Yisrael is challenged by Hashem to rely on Him and Him alone.
These circumstances can be viewed as tests from Hashem, tests that the Jews failed one hundred percent, causing the sinful behavior that followed.
Yet, in their defense, the Jewish people perceived themselves during those periods as being in a state of national crisis. Was it easy for a nation so dependent on Moshe to deal with the possibility of continuing on in the wilderness without his leadership? Was it easy for a people, unaccustomed to fighting, to envision conquering the land of Israel?
They may have done poorly on these exams, but even the process of failing can be a source of future strength. Moshe, therefore, pleads again and again with Hashem to give them another chance.
Korach and his followers, though, did not deserve that second chance.
It is one thing to face a challenge and fail. But to create a crisis, to sow the seeds of disunity within the Jewish people, to generate strife and unnecessarily challenge the leadership of the Jewish people, these sins cannot be excused or forgiven.
Korach took his personal agenda and planted it on the national stage. He put Klal Yisrael at risk. This type of threat can not be overlooked or tolerated.