The article you were assigned to read was written by Mustafa Akyol, a Turkish journalist who has covered these issues in greater depth in his 2011 book, Islam Without Extremes: A Muslim Case For Liberty. The article itself, "How Politics Has Poisoned Islam", was published as an opinion piece in the New York Times on 3 February 2016.
In this article, Akyol argues that the politicization of Islam began quite early in the history of the religion, just after the death of the Prophet Muhammad. He recounts the issue of the original debates leading to the split between Shia and Sunni Muslims. The division was not religious, but a political one over who should become caliph, a position that fused religious authority and political power.
Abu Bakr, a friend of Muhammad and father of Muhammad's wife Aisha became the first caliph of what has evolved into Sunni Islam, the sect to which most contemporary Muslims belong. The Shia believe that Ali ibn Abi Talib should have been the first caliph. Overall, the Sunnis are far more numerous and powerful than the Shia, constituting approximately 85 to 90 percent of Muslims globally. Akyol argues that these two groups do not differ significantly in their actual religious faith.
In the Middle East, Saudia Arabia and the other Gulf states, Egypt, and Jordan are primarily Sunni, with Iran being the major Shia power. This division is exacerbated by ethnic and linguistic differences, with Iran being mainly Persian (and thus Indo-European in language) with Azerbaijani and Kurdish minorities and the Gulf states and Egypt being Arabic; Turkey, of course, was conquered by the Turks, a group from Mongolia, in the middle ages.
Akyol next moves on to the Ottoman (Turkish) Empire, suggesting that it added a component of western liberal democracy to the politics of Islamic states in the Middle East.
His point, which is emphasized through the entire article, is that divisions among Muslims are not ones of religious belief as all Muslims agree on the pillars of faith, and thus that they are not an inherent part of Islam, but rather political in nature. He suggests that Islam is best practiced in an atmosphere of religious freedom, and concludes with the statement:
But when Islam merges with power, or becomes a rallying cry in power struggles, its values begin to fade.