Then the Jews began to argue sharply among themselves, “How can this man give us his flesh to eat?”
“argue” = emachonto = to fight in armed combat. There was a difference of opinion as to the words of Jesus. There were many who were strongly for Him but from what was asked of Him it may be seen that there were many more that were not. These differing viewpoints were being expressed in a war of words.
“How can” = the same idiom used by Nicodemus in John 3:4,9 but probably with a different tone of voice. Although it expresses disbelief and misunderstanding in both places, here it is used with a large measure of scorn.
“this man” = used contemptuously.
They cannot understand how Jesus could give them his flesh to eat. They miss the spiritual significance of his words.