Because it would mean denying Islam itself
In June 2009 at al-Azhar, Barack Obama said: “For over a thousand years, Al-Azhar has stood as a beacon of Islamic learning.”
In October 2001, right after 9/11, the New York Times called Al-Azhar “the revered mosque, the distinguished university, the leading voice of the Sunni Muslim establishment.” It quoted a Muslim cleric: “Al Azhar is the only institution in the world that has learned the moderate Islam and taught it in a moderate way without fanaticism, and without abiding by the teachings of a school that promotes rigidity or violence.”
So why doesn’t al-Azhar declare the Islamic State apostate? Non-Muslim authorities all over the West assume that the vast majority of Muslims reject and abhor the understanding of Islam taught by the Islamic State. Why doesn’t the foremost institution in Sunni Islam validate that assumption? Because they know that what the Islamic State is doing has ample justification in Islamic texts and teachings. The beheadings (Qur’an 47:4); the subjugation of Christians as dhimmis (Qur’an 9:29) or the massacre of Christians who refused to submit (Qur’an 9:5); the sexual enslavement of infidel women (Qur’an 4:3, 4:24, 23:1-6, 33:50, 70:30) — it’s all there.
“Why does Egypt’s largest Muslim beacon, Al-Azhar, refuse to declare IS ‘apostate’?,”
by Taha Saker, Egypt Independent, April 14, 2017:
After the Islamic State (IS) militant group declared its responsibility for Palm Sunday’s deadly attacks that targeted two Coptic churches in Egypt’s Delta and Alexandria city, several media figures and organizations launched severe attack against Egypt’s largest religious institution, Al-Azhar University, considering its teachings as fostering religious extremism.
Through these outlets, Al-Azhar is now facing the backlash of taking part in supporting the IS-affiliated members through its insistance [sic] to refuse considering the IS group as ‘apostates’ and through maintaining some extremist teachings in the syllabuses that are taught to its students.
The backlash criticized the educational syllabuses that are being currently taught in Al-Azhar institution that include teachings from some prominent clerics. These teachings directly incite the brutal killing of anyone who does not follow Islam or who had been deemed to be an ‘infidel’.
The criticism, released from those figures and other media outlets, accused the aforementioned teachings of Al-Azhar by increasingly contributing to generate numerous members affiliated to IS.
Moreover, Al-Azhar’s teaching are perceived by some as the main platform that legitimizes the killing and slaughtering which are currently being practiced by IS group in different parts of the world, in the name of Islamic (Sharia) law….