The identification of the Quran's "Holy Spirit" with Gabriel is not stated in one explicit sentence, but it is not textually baseless. It is a reasoned conclusion from the Quran's wider vocabulary, its descriptions of revelation, and the explanations transmitted in classical tafsir.
Why the objection seems plausible
The critic is right about one limited point: the Quran does not say, in the form "the Holy Spirit is Gabriel." It uses several expressions: "the Holy Spirit" (Ruh al-Qudus), "the Trustworthy Spirit" (Ruh al-Amin), and Gabriel by name. Since these expressions are not always placed in direct apposition, a reader may argue that they refer to different beings.
The argument from 16:2 also deserves to be stated fairly:
He sends down the angels with the Spirit of His command upon whom He wills among His servants...
Quran 16:2
If "the spirit" necessarily meant one of the angels, the critic asks, why mention both "the angels" and "the spirit"? This is a real interpretive question, not something to dismiss casually.
What the Quran actually supports
The word ruh is broader than the English word "spirit." In the Quran it can refer to revelation, divine command, or a particular created spirit. Therefore, the phrase "with the Spirit of His command" does not by itself require a separate non-angelic being. It may describe what the angels carry, the command by which they descend, or an accompanying agent. Arabic prepositions do not always settle such questions by themselves.
In 16:102, the Holy Spirit is said to bring down the Quran:
Say, "The Holy Spirit has brought it down from your Lord in truth, to strengthen those who believe, and as guidance and good news for the Muslims."
Quran 16:102
Elsewhere, the Quran describes the revelation as brought by "the Trustworthy Spirit":
And indeed, it is a revelation brought down by the Trustworthy Spirit upon your heart, so that you may be among the warners.
Quran 26:193-194
And Gabriel is explicitly the one who brings revelation to the Prophet:
Say, whoever is an enemy to Gabriel - it is he who has brought it down upon your heart by Allah's permission...
Quran 2:97
What this establishes - and what it does not
These verses do not provide a simple dictionary-style equation. The identification is an interpretive conclusion: the same revelatory role is attributed to the Holy Spirit, the Trustworthy Spirit, and Gabriel. This is why al-Tabari, Ibn Kathir, and other major commentators understood Ruh al-Qudus in these revelation passages to mean Gabriel.
Nor does 16:2 refute that conclusion. It mentions angels and the Spirit together, but "the angels" may be a general category while Gabriel is a particular angel, or "the spirit" may mean the revelation or divine command accompanying their descent. Thus the objection shows that the Quran uses ruh in more than one way; it does not establish that the Holy Spirit cannot be Gabriel in the relevant passages.