Church Fathers on John 15:3

He rises in haste to perform the sacrament of His final passion in the flesh (such is His desire to fulfill His Father’s commandment) and therefore takes occasion to unfold the mystery of His assumption of His flesh, whereby He supports us, as the vine does its branches: I am the true vine.

He says this as being the Head of the Church, of which we are the members, the Man Christ Jesus; for the vine and the branches are of the same nature. When He says, I am the true vine, He does not mean really a vine; for He is only called so metaphorically, not literally, even as He is called the Lamb, the Sheep, and the like; but He distinguishes Himself from that vine to whom it is said, How you are turned into the degenerate plant of a strange vine to me (Jer 11:21). For…

And forasmuch as Christ was sufficient for Himself, but His disciples needed the help of the Husbandman, of the vine He says nothing, but adds concerning the branches, Every branch in Me that bears not fruit, He takes away. By fruit is meant life, i.e. that no one can be in Him without good works.