Because the Western Patriarch (or Pope) is the Bishop of Rome.
In antiquity there used to be the Pentarchy, there were five major and significant centers of Christianity: Jerusalem, Antioch, Alexandria, Constantinople and Rome. Each was significant for various reasons.
Jerusalem was "Mother of all the churches" whose Patriarch was successor of the Seat of St. James.
Antioch was the second major place of apostolic activity, where we were first called "Christians" and the Patriarch was successor of Sts. Peter and Paul.
Alexandria was where the Catechetical School was founded, and was a significant hub of learning in the Greco-Roman world, and that also ended up including Christian learning. The Patriarch was successor of St. Mark the Evangelist.
Rome was capital of the Roman Empire, as such the bishop there was, in a sense, in the thick of what was going on in the world. The Patriarch was successor of St. Peter.
Byzantium became Constantinople and thus New Rome, the Patriarch of Constantinople was successor of St. Andrew.
Of these five Rome held a certain significant place, since much of the theological controversies that the Church faced arose in the East, the Bishop of Rome was often sought for his counsel on matters. Perhaps due to being able to be more impartial since Rome was of significant distance from the centers of these disputes.
After the collapse of the Western Empire significant historical events happened that both shaped the Church as well as Western Europe in general.
Firstly: Without a centralized civil authority the Bishop of Rome was often sought as an island of stability, and as Germanic kings and warlords fought one another the Church in Rome remained rather fixed and he was often sought for appeal.
Secondly: The liturgies of the West slowly became more standardized, being brought into conformity with the Liturgical Rite used in Rome (the Latin Rite). Part of this process ended up involving a change in the language of the Nicene Creed. A single word was added in the Liturgical Rite used among the Frankish people of Gaul, "Filioque". Originally the Bishop of Rome opposed this change, but over time it was adopted into the Roman Liturgy and disseminated as part of the liturgical standardization throughout Western Europe.
Thirdly: Muslim conquests of Byzantine lands not only meant less power for the Roman Emperor in Constantinople, but also meant that the Patriarchs were increasingly more separated. By the 11th century the only Patriarch still in Byzantine/Roman territory was the Patriarch of Constantinople.
Fourthly: Even prior to the Fall of Rome and collapse of the Western Empire Latin had begun to replace Greek as the dominant language. This caused linguistic barriers between East and West, between Greek theologians and Latin theologians. Theological and Liturgical differences which had been present in some form for some time became more significant. In effect this compounded other factors which led to a growing rift within the Church.
Fifthly: In the beginning of the 9th century the Bishop of Rome crowned Charlemagne the Holy Roman Emperor. This was no small matter as the Byzantine Emperor still claimed Western Europe as part of his domain. This, in a sense, meant that there were two Roman emperors, one Byzantine and one Frankish. This did not, by any means, help relations between the East and the West.
Sixthly: Originally the use of the word "pope" (meaning "papa") was a term of endearment applied to a bishop by the people. The Bishop of Rome wasn't the first or only to have this term applied, even to this day the Patriarch of Alexandria is referred to as "Pope" (c.f.
Pope Shenouda III). In the 5th century Pope Leo I seems to have been the first to claim it as an exclusive title for the Roman Patriarch.
Seventhly: All of these factors ended up erupting in the middle of the 11th century. For one, the Pope argued that he had a primacy of jurisdiction (not just of honor as the East had traditionally taught), and insisted the authority to add the Filioque clause into the Creed apart from the need of an Ecumenical Council. The Patriarch of Constantinople rejected these claims. In 1054 two representatives of the Pope went to Constantinople and laid a Bull of Excommunication--the Patriarch of Rome had excommunicated the Patriarch of Constantinople. Outraged, the Patriarch of Constantinople returned the favor and excommunicated the Patriarch of Rome.
The Great Schism had just happened.
Both sides claim to be right. Both sides claim to be the True Church founded by Christ and that the other has broken away. Both claim to be
the One, Holy, Apostolic and Catholic Church.
What this, of course, meant in the West was that there was now only one Patriarch, the Pope in Rome.
In usual Roman Catholic parlance "Roman" simply refers to the Liturgical Rite, the Roman or Latin Rite. Eastern or Byzantine Catholics are those in communion with Rome who use the Byzantine Rite (and so on and so forth).
Though, arguably, among most Protestants and Orthodox the term "Roman" in the Roman Catholic Church refers also to the fact that it is constituted in part by being in ecclesiastical union with the Roman See.
In any event "Roman" has to do entirely with geography--the city of Rome. It has nothing to do with Constantine or the Roman Empire.
-CryptoLutheran