The word used for eat in John 6:53 is not "esthio" but "phagein."
Check your Greek New Testament.
ἐσθίω,v {es-thee'-o} 1) to eat 2) to eat (consume) a thing 2a) to take food, eat a meal 3) metaph. to devour, consume
http://www.greekbible.com/l.php?e)sqi/w_v-2aas-p--_p
http://www.greekbible.com/index.php
Phagein not used in this verse.
esqiw,v {es-thee'-o}
It looked the same on another online bible I checked. I have to note that I don't read greek. But I know how to recognize some letters, and input words into lexicons.
It just seems odd that we are having an argument over which word is in the greek. Is it possible we have different greek bibles, and the one you use supports your contention?