"Jesus said the Father is greater than him"

Jesus himself said, "the Father is greater than I" (John 14:28). He could not be clearer. The Son is lower than the Father. That is not equality.

The word is meizōn — "greater." It is not kreissōn, "better" or "superior in nature." Greek had a word for a claim about rank of being, and John does not use it. In the same discourse, a few verses earlier and later, Jesus says the Father and he mutually indwell one another, that seeing him is seeing the Father, and that everything the Father has is his. A being who is merely lower does not say those things. So whatever "greater" means, it has to fit alongside them.

You are just explaining away the plain words. Why would he say "greater" at all if they are equal?

Read the whole sentence: "If you loved me, you would rejoice that I am going to the Father, because the Father is greater than I." The reason for their joy is that he is returning to the Father — leaving the condition of humiliation, hunger, weariness and coming death, and going back to glory. "Greater" describes the Son as he now is, in the flesh, on the way to the cross — not the Son as he eternally is. The Nicene reading-rule, stated plainly by Gregory of Nazianzus, is that texts which sound lowly are said of the incarnate Son, and texts of full deity of the same Son as God. One person, two states.

That still leaves the Father as the source. If the Son comes from the Father, the Father is prior — and prior means greater in the ordinary sense.

The tradition agrees the Father is the source — the unbegotten one, the fount of the Godhead — and this is exactly where "greater" also points: greater as origin, not greater as being. The Son is eternally begotten, receiving the one undivided divine nature from the Father without ever beginning to exist and without being less than what he receives. Origin within God is not superiority of nature, any more than a spring is a better kind of water than the river. This is why the same fathers who insist the Father is the source also insist the Son is "true God from true God" — equal in nature, distinct in relation.