Two criticisms come up often:
Some see a scientific error in this verse:
“Until, when he reached the setting of the sun, he found it setting in a spring of dark mud, and he found near it a people. Allah said: ‘O Dhul-Qarnayn, either you punish [them] or else adopt among them [a way of] goodness.’”— Surah Al-Kahf (18:86)
The Quran does not say that the sun actually sets in a spring.
It says: “he found it” — meaning from Dhul-Qarnayn's point of view.
It is like saying: “The sun rises.” That is a visual perception, not a physical reality.
Sunnism does not rely solely on the Quran — it also includes the Sunnah and the Ijma.
The Quran gives shares for distributing inheritance (non-exhaustive list):
If a man leaves:
The total is 2/3 + 1/6 + 1/6 = 6/6.
If a man leaves:
And if we add these shares: 1/8 + 2/3 + 1/6 + 1/6 = 27/24.
You cannot give 27 slices of a cake that has only 24.
The legal method applied in this situation is called Al-Awl.
It is a proportional reduction. The cake is no longer in /24, it becomes /27. The wife therefore receives 3/27, the daughters 16/27, etc. The total is 100% and the proportion between the shares is respected.
The criticism claims that this method is a problem, since it is not mentioned in the Quran.
But it was the Prophet ﷺ himself who designated Zayd as the authority on inheritance matters.
And when this case (27/24) arose, the Companions unanimously agreed (Ijma) to apply Al-Awl.
The criticism only makes sense if one rejects the Sunnah and the Ijma.
But rejecting them is not a criticism of Sunnism, but rather of the Quranist methodology .