The Eastern Orthodox Churches lack two of the notes of the Church we profess in the Creed: they are not “one” nor are they “catholic.” These notes are interelated (you can’t really have one without the other).
The jurisdiction of the papacy is necessary for the Church to be one. The Eastern Orthodox Churches are a perfect example of why this is. They get into situations where EO Church A is in communion with B, B is in communion with C, but A and C are not in communion with each other (A=B=C≠A) (e.g. the Moscow Patriarchate breaking communion with Constantinople over who had jurisdiction over Estonia in 1996 while other Churches remained in communion with both; ROCOR’s situation until 2006; the Bulgarian schism of the 19th century when most patriarchates, but not Moscow, broke communion with the Bulgarian Church, etc., etc.). How can one Church simultaneously have some parts in communion with other parts, while other parts are separated from each other? This doesn’t even make any sense unless there is only a plurality of Churches, rather than just one.
Also, look at the recent pan-Orthodox Synod (or whatever it ultimately was classified as). It barely even got off the ground because Churches were threatening to boycott (and many did) because they were fighting with other Churches over who had jurisdiction over what. And for all the EO polemics about all bishops being equal, if you look at how that synod was explicitly organized and carried out, the bishops who participated in that synod did not do so as equal bishops of one Church, but as representatives of multiple national Churches and patriarchates. What was sought was not a consensus of the bishops of one Church (or even a consensus of particular Churches), but rather a consensus of national Churches/patriarchates (which didn’t happen anyway).
Because without the primacy they lack this oneness, they also have had to embrace a purely eucharistic ecclesiology, rejecting any universal ecclesiology. They now mostly only acknowledge the eucharistic or particular Church (a bishop, assisted by his priests and deacons, and the flock entrusted to him) as the only true manifestation of the Church of Christ. Catholics acknowledge both the reality of the particular Church and the universal Church, as the Fathers did. The Fathers used the term “catholic” to differentiate when they were talking about the whole Church throughout the world, rather than a particular Church (e.g. Church of Corinth, Church of Ephesus, Church of Rome, Church of Antioch, etc.). The EOs now reject an ecclesiology that acknowledges a catholic Church.
By rejecting the primacy, the EO Churches are not one Church and as a result, they must deny the ecclesiastical reality of the catholic Church. The Catholic Church is one and acknowledges the catholic Church and the particular/eucharistic Churches.