It does not “become” the body and blood of Christ? You mean the bread and wine were always the body and blood of Christ, before he said they were?
I do not presume to interpret His words. I just accept them as He said them.
And whilst they were at supper, Jesus took bread and blessed and broke and gave to his disciples and said: Take ye and eat. This is my body. And taking the chalice, he gave thanks and gave to them, saying: Drink ye all of this. For this is my blood of the new testament, which shall be shed for many unto remission of sins.
(Matthew 26:26-28 DRB)
And whilst they were eating, Jesus took bread; and blessing, broke and gave to them and said: Take ye. This is my body. And having taken the chalice, giving thanks, he gave it to them. And they all drank of it. And he said to them: This is my blood of the new testament, which shall be shed for many.
(Mark 14:22-24 DRB)
And taking bread, he gave thanks and brake and gave to them, saying: This is my body, which is given for you. Do this for a commemoration of me. In like manner, the chalice also, after he had supped, saying: This is the chalice, the new testament in my blood, which shall be shed for you.
(Luke 22:19-20 DRB)