It would be more accurate to say, not that Christ is the incarnation of the Second Person, but that Christ is the Second Person incarnate; indeed Christ is the Christian Name for the Second Person as such, whether incarnate or not—the Name, in other words, for the Logos “by whom all things were made” and the “light of men”. You may wish to read, or re-read, my short article on “Perennial Philosophy and Christianity“, which raises the question of other avataric manifestations of the “only Son”.
Why do “we” base our religion as Christians on the Second Person? Because God did! God became man, and in so doing He made it possible for man to “become God” through a sacramental assimilation of His “real presence”. From a point of view that accentuates the Divine Transcendence, the Second Person might seem to be “second best”, a kind of compromise or lessening of the metaphysical Absolute; but from a point of view that accentuates the Divine Immanence, the Christian possibility can be seen as the superior Way inasmuch as the possibility of deification is placed front and center.
Schuon writes, “Esoterically speaking, there are only two relationships to take into consideration, that of transcendence and that of immanence: according to the first, the reality of Substance annihilates that of the accident; according to the second, the qualities of the accident—starting with their reality—cannot but be those of Substance.” If Islam stresses the first relationship and Christianity the second, we must nonetheless remember that Transcendence is immanent, and Immanence is transcendent.