The Greek word used for "feeds" here is very blunt and has the sense of "chewing" or "gnawing." His listeners must have been stupefied. It is the same Greek word used in John 6:54 where Jesus proclaims, "Whoever feeds on my flesh and drinks my blood has eternal life, and I will raise him up on the last day." The use of such strong language is why early Christians were accused of cannibalism (i.e., Minucius Felix, Octavius ch. 9, 2nd or 3rd century).
Modern English translations are reluctant to use such graphic language, perhaps so as not to arouse strong adverse reaction. But vigorous reaction on our part is precisely what is needed here and what Jesus wants. Once we truly grasp the hopelessness and helplessness of our fallen condition, rather than a polite and reserved "partaking", we will claw our way to Jesus and gnaw hungrily on His atoning, life-giving sacrifice. The picture is of a starving pitiful man at the point of death desperately and voraciously chewing on life-giving, raw flesh and blood - not of a refined gentleman in a coat and tie in his Sunday-morning best in comfortable pews, gently and quietly partaking of a wafer and a sip of grape juice accompanied by pleasant background music.
Chew voraciously and gnaw on Christ's atoning sacrifice. It's your only realistic deliverance out of the madness and chaos of this fallen world; everything else is hopelessly futile.