The argument is really about transubstantiation. This is an answer to a how question. It is the answer provided by Aquinas.

Well, Aquinas did assent to transubstantiation, and worked out some of the more specific Aristotelian implications of it for the philosophical orthodoxies of his own time, but it wasn't his idea in the first place and he had nothing to do with its getting adopted as official church doctrine.

The idea that the body and blood are really, literally there in the Eucharist was affirmed by Paschasius Radbertus in the Ninth Century, and the discussions which led to the emergence of the theory of transubstantiation were stirred up by Berengar of Tours, Roscelin of Compiegne and Peter Abelard in the first half of the Twelfth Century. The earliest use of the term transubstantiation for this explanation of the phenomenon comes from Hildebert of Lavardins (d. 1133). The competing explanations at the time were consubstantiation and annihilationism, which I discussed at http://richarddawkins.net/articles/645493-in-defense-of-dawkins-s-reason-rally-speech/comments?page=1#comment_931881.

The church adopted "transubstantiation" as its official doctrinal formula at the First Lateran Council of 1215. Aquinas was born ten years later in 1225.

It is a common mistake to make, attributing everything in Medieval theology to Aquinas. People tend to make it because Aquinas was elevated to something like chief theological authority of the Middle Ages by nineteenth century French catholics, and as a result he's pretty much the only major Medieval theologian or philosopher anyone has ever heard of.