A key thing to keep in mind is that Kant differentiated logical from metaphysical, or analytical from synthetical, necessity. The principle of the transcendental unity of apperception is, he says, analytical, despite having an important role in synthesis (not quite the same thing as syntheticality, I should note).
Had he claimed that the principle was synthetical, he would have had to say that we have an intuition of permanence also, here, which we do not (as he goes on to explain with respect to the paralogism). For that permanence would be the synthetical necessity which would render the "I think" a true substance.
To (try to) clarify matters further: Kant distinguished the logico-functional form of categorical judgments from the category of substance proper, even though the latter has its formal grounding in the former(!). Aristotle had defined a substance as that which must always be a subject and never a predicate only (you should see here where Kant got the second formulation of the categorical imperative from, mind you). Kant agrees far enough to find the structural grounds for his definition of substance in Aristotle's definition, but doesn't hesitate to add that intuition must be superadded to this definition to make it metaphysically, and not just logically, viable. And so again, this intuition is lacking, here (the "I think" is too general to be an intuition; the word "I" here is not intuitively grounded in me (or you, or anyone else) in particular, but is a general accompaniment of any thinking being's apperception).