The argument identifies a real philosophical tension only if "free will" means the ability to choose between good and evil in exactly the same way human beings do. Islam does not accept that definition as necessary, nor does it regard Allah's goodness as a restriction imposed by something outside Him.
Why the argument seems forceful
The critic's case can be stated strongly. A free agent, it is said, must have genuine alternatives. If Allah can choose freely, He must be able to choose injustice, deception, or cruelty. Yet a maximally good being cannot do any of these things. Therefore, the critic concludes, Islamic teaching seems to affirm both that Allah can do evil and that He cannot do evil.
This would be a contradiction if two assumptions were granted: first, that freedom necessarily includes the power to perform moral evil; and second, that inability to do evil is a defect in freedom. Neither assumption is self-evident.
What divine freedom means in Islam
The Quran affirms Allah's unrestricted sovereignty and will:
He is the Doer of whatever He wills.
Quran 85:16
But this does not mean that every logically describable act is a real possibility for Him. We commonly say that a truthful person is free to speak, while not treating the ability to lie as necessary for freedom. A person who cannot betray a loved one because of firm character has not thereby lost all agency. Freedom means acting knowingly and willingly, not being morally defective.
In Islamic theology, Allah's will is not an arbitrary power detached from His attributes. He wills with knowledge and wisdom, and His perfection excludes injustice. The Quran says:
Indeed, Allah does not do injustice, even as much as an atom's weight.
Quran 4:40
It also says:
He is not questioned about what He does, but they will be questioned.
Quran 21:23
The first verse denies injustice; the second denies that Allah is subject to a superior judge or external moral law. These statements are compatible. Allah is not forced to be good by a power above Him. Rather, goodness and justice belong to His perfection, while injustice is contrary to what He is.
Does "can" have only one meaning?
The argument moves between different senses of possibility. Allah has power over all things, but absurdities are not "things": a square circle is not an unrealized object awaiting divine choice. Likewise, divine inability to be unjust is not a limitation caused by weakness. It is the necessary consequence of perfect knowledge, wisdom, and goodness.
The Prophet Muhammad (PBUH) conveyed this in a hadith qudsi:
O My servants, I have forbidden injustice for Myself and made it forbidden among you, so do not wrong one another.
Sahih Muslim
Thus, the argument does not establish an incoherence in Islam. It shows only that Islamic theism rejects the premise that freedom requires the capacity for evil. Allah is free because He acts by His own will, and perfectly good because His will is never corrupted by ignorance, need, or injustice.