Clearly, the breaking the bread and identifying it explicitly as His body, is not a game of cherades. And no Christian ever said as much until very recently (with the merely commemorative, 'symbolic' or consubstantial presence views of the Eucharist, where the bread is paraded around as, and called, His flesh, while being no different from any other bread).
There is of course a variant here about the presence of the word 'broken,' but supposing it is original, when He breaks the bread and says He is breaking His body (the verbs are neuter, referring to the body, rather than the bread, masculine, being broken), it is because He has identified the bread as His body, not because His body was broken elsewhere except in this sense. He breaks the Eucharistic bread turned His body. This is quite different from a breaking of His body, e.g. on the Cross.
... For you have just heard him say distinctly, That our Lord Jesus Christ in the night in which He was betrayed, took bread, and when He had given thanks He broke it, and gave to His disciples, saying, Take, eat, this is My Body: and having taken the cup and given thanks, He said, Take, drink, this is My Blood. Since then He Himself declared and said of the Bread, This is My Body, who shall dare to doubt any longer? And since He has Himself affirmed and said, This is My Blood, who shall ever hesitate, saying, that it is not His blood? ... Consider therefore the Bread and the Wine not as bare elements, for they are, according to the Lord's declaration, the Body and Blood of Christ; for even though sense suggests this to you, yet let faith establish you. Judge not the matter from the taste, but from faith be fully assured without misgiving, that the Body and Blood of Christ have been vouchsafed to you. ... Having learned these things, and been fully assured that the seeming bread is not bread, though sensible to taste, but the Body of Christ; and that the seeming wine is not wine, though the taste will have it so, but the Blood of Christ1
1 Cyril of Jerusalem, Catechetical Lecture 22