The argument correctly sees that love is ordinarily directed toward someone, but it does not show that God must contain multiple persons in order to be loving. It confuses an eternal attribute with the created objects and temporal acts through which that attribute becomes manifest.
Why the objection seems powerful
The strongest form of the objection is this: if Allah is absolutely solitary before creation, there is no other being for Him to love, show mercy to, or have compassion toward. If these qualities only become meaningful once creatures exist, then Allah's love appears to be a new response caused by creation. A God whose inner life already contains distinct persons, the argument continues, can love eternally without depending on anything created.
That is a serious philosophical question, not a foolish misunderstanding. It depends, however, on treating "love" as though it can only mean an already-exercised relationship with a distinct creature.
Attribute, object, and act are not the same thing
Islam distinguishes between Allah's perfection and the created effects of His actions. Allah's knowledge is eternal, while particular events come into existence in time. His power is eternal, while particular acts of creation occur when He wills. Likewise, His mercy and love are not acquired qualities produced by creatures. The objects of mercy are created, and the particular act of mercy occurs in time, but Allah does not become more perfect when that act occurs.
"And He is the Forgiving, the Loving."
Quran 85:14
Classical scholars therefore distinguished Allah's essential attributes from the temporal effects of His will. The sun does not gain the attribute of brightness when a room is opened; rather, its existing brightness becomes manifest there. The analogy is limited, but it shows the logical distinction. A relation can be new on the side of the creature without being a newly acquired perfection in God.
Nor does Islamic monotheism require Allah to be emotionally needy or dependent on an object. Human love often includes need, vulnerability, and change. Divine love is a perfection of will, generosity, approval, and favor, not an unfulfilled lack that creation repairs. The Quran also states:
"Say: He is Allah, One. Allah, the Eternal Refuge. He neither begets nor is born, nor is there to Him any equivalent."
Quran 112:1-4
What this argument does and does not establish
The argument may establish that a loving God has a real relation to what He loves. Islam affirms that relation after creation. It does not establish that this relation must be eternal, or that it must exist between multiple divine persons. If creation is freely chosen, its coming into existence can be contingent without making Allah's perfection contingent. And even if eternal interpersonal love were shown to be necessary, that would not by itself prove three persons, rather than some other proposed account.
So the objection highlights a difference between Islamic and Trinitarian understandings of divine love, but it does not refute the Islamic view. Allah is eternally perfect and loving; creatures are temporal recipients of a love that was never an acquired need.