Iraq has both Christians of the original Orthodox Church and those who for various reasons chose to leave their ancestral church or were enticed to leave. Here is a brief historical background. As with other Orthodox in the Middle East, often the Catholics used schools as a bridge to entice Orthodox to leave their church. I have met Copts in Canada whose parents and grandparents went to the only available schools run by Catholic missionaries and were forced to undergo a Catholic ceremony of "First Communion" as well as being indoctrinated in Catholic theology as the price for education which enabled them to move up the social scale.
Here is a brief background:
"The Syrian Catholic Church is an offshoot of the Assyrian Apostolic Church (changed in the 1950s to the Syrian Orthodox Church), popularly known as Jacobite. The conversion of parts of the Jacobite community to Catholicism began in the 17th century but took about two centuries to stabilize. The movement was centered in Ottoman Aleppo (now in Syria) operating under the influence of French diplomats and missionaries. Today the head of this Church, the Patriarch of Antioch (one of many), resides in Beirut. The language of this community is Syriac and Arabic for liturgy and for vernacular use. With a considerable portion of the community is diaspora outside the Middle East , the main communities in the Middle East are located in northern Iraq (around Mosul), in the Aleppo area, and in Lebanon.http://en.wikipedia.org/wiki/Talk:Syriac_Catholic_ChurchThe formation of the Church
During the Crusades there were many examples of warm relations between Catholic and Syriac ("Syrian") Orthodox bishops. Some of these bishops seemed favourable to union with Rome, but no concrete results were achieved. There was also a decree of union between the Syriac Orthodox and Rome at the Council of Florence November 30, 1444 but the effects of this decree were rapidly annulled by opponents of the union among the Syriac hierarchy.
Jesuit and Capuchin missionaries began to work among the Syriac Orthodox faithful at Aleppo in 1626. So many of them were received into communion with Rome that in 1662, when the Patriarchate had fallen vacant, the Catholic party was able to elect one of its own, Andrew Akhidjan, as Patriarch of the Syriac Church. This provoked a split in the community, and after Akhidjan’s death in 1677 two opposing patriarchs were elected, one being the uncle of the other, representing the two parties (one pro-Catholic, the other anti-Catholic). But when the Catholic Patriarch died in 1702, this very brief line of Catholic Patriarchs upon the Syriac Church's See of Antioch died out with him.
The Ottoman government supported the Syriac Orthodox's agitation against the Syriac Catholics, and throughout the 18th century the Syriac Catholics underwent suffering and much persecution. There were long periods when no Syriac Catholic bishops were functioning, and the community was forced to go entirely underground.
In 1782 the Syriac Orthodox Holy Synod elected Metropolitan Michael Jarweh of Aleppo as Patriarch. Shortly after he was enthroned, he declared himself Catholic and in unity with the Pope of Rome. After this declaration Jarweh took refuge in Lebanon and built the still-extant monastery of Our Lady at Sharfeh. Since Jaroueh there has been an unbroken succession of Syriac Catholic Patriarchs.
In 1829 the Turkish government granted legal recognition to the Syriac Catholic Church, and the residence of the Patriarch was established at Aleppo in 1831. Catholic missionary activity resumed. Because the Christian community at Aleppo had been severely persecuted, the Patriarchate was moved to Mardin (now in southeast Turkey) in 1850.
The steady Syriac Catholic expansion at the expense of the Syriac Orthodox was ended by the persecutions and massacres that took place during World War I (Assyrian genocide). More than half of the 75,000 Syriac Catholics were massacred by Turkish nationalists (especially so-called Young Turks). In the early 1920s the Catholic Patriarchal residence was therefore moved to Beirut, to which many Syriac Catholics had fled from Turkish and intra-Syria terror.
The Syriac Catholic Patriarch always takes the name "Ignatius" in addition to another name. Although Syriac Catholic priests were bound to celibacy by the Syriac Catholic local Synod of Sharfeh in 1888, there are now a number of married priests. A patriarchal seminary and printing house are located at Sharfeh Monastery in Lebanon."http://en.wikipedia.org/wiki/Syrian_Catholic_Church