I am in communion with the Melkite Catholic Church, and the bishop of Rome happens to be in communion with the same Church.The Melkite Church commemorates the Pope at every liturgy (not just at special events or when the Pope is present at the liturgy). One does that only for a hierarch who has jurisdiction over one's church. Therefore, the Melkite church acknowledges the Pope's universal jurisdiction at every liturgy. If you are still confused about what your church teaches, here is a helpful link: https://melkite.org/eparchy/bishop-john/what-is-the-relationship-between-the-melkite-clergy-and-the-pope-why-and-how-is-the-pope-commemorated-in-the-melkite-church
Rather than write my own response I thought I would re-post the text written by Hesychios:
"Looks like equal time given to opposing viewpoints...
Bishop John Elya was one of only two Melkite bishops in the synod to vote against the Zoghby initiative. Both of whom were appointed to their positions by the Pope, not the Melkite synod!
In other words, the Pope now (only since Vat II) has the power to name members to the Melkite synod, when those Sees are in the diaspora. I hate to state that bishop John's opinion can be discounted, clearly it cannot, but he is equally clearly out of step with his own synod and Patriarch, as well as (apparently) traditional Melkite belief.
He is also retired, and no longer occupies the See. I wonder if his successor was a bishop at the time, and if he signed the Zoghby Initiative? Can anyone here help us with that?
Nevertheless, the initiative passed overwhelmingly, and was heartily endorsed by the Patriarch. Bishop John does not speak for anyone but himself (and his Pope I guess, that counts for something), he is contradicting his church's Synod.
We see the Melkites saying one thing in the synod, and another in the diaspora. It's synodal integrity slowing eroding away as more and more Melkites leave the Middle east for places like Europe, Australia and North America and the Pope will have ever growing direct control over erecting new Eparchies and appointing new bishops.
Why is this important? Patriarchal churches in Communion with Rome must be absolutely free of coercion from, or subordination to the See of Rome, to set a good example for the Orthodox. Right now we see a synod with manacles on, making a lot of noise but ultimately unable: to even name all it's own bishops, manage it's own growth and teach it's own Truth to it's children abroad.
No Orthodox church wants to be trapped in a vortex like that one, enticed by promises then slowly constrained into absorption, and with that Orthodox Truth disappears. Michae