Islam vs Christianity: Claim: God is not triune

While Islam refers to Christians as "people of the book" along with Jews and Zoroastrians (as opposed to polytheists and animists), it denies that Christianity is the final and permanent revelation of God and speaks quite negatively of Christians as "the infidels" (kaffur). This is because Muhammad, "the seal of the prophets," is the last and greatest of the prophets of Allah (Qur'an 48:27-28). He alone corrects the errors of the past, including the aberrations of Christianity. Islam abrogates Christianity (Qur'an 48:27-28); it is Christianity's replacement. The argument for abrogation  is rooted in five major claims made by Islam against Christianity. This is a significant apologetic challenge that Christians today need to face intelligently, given the global reach of Islam and its growing influence in the West.

Claim 4: God is not triune. Islam denies that God is triune, affirming that Allah is absolutely one, without son or partner. Any other doctrine is abominated as polytheism.

Certainly they disbelieve who say: Surely Allah is the third (person) of the three; and there is no god but the one God, and if they desist not from what they say, a painful chastisement shall befall those among them who disbelieve. (Qur'an 5:73)

The Qur'an misunderstands the nature of the Trinity as presented in Scripture. While the Bible speaks of one God (Deuteronomy 6:4) and three persons who are divine-Father, Son and Holy Spirit-the Qur'an's interpretation of the Bible leaves out the Holy Spirit and deems Mary one of the divine persons.

And when Allah will say: 0 Isa son of Marium! did you say to men, Take me and my mother for two gods besides Allah he will say: Glory be to Thee, it did not befit me that I should say what I had no right to (say); if I had said it, Thou wouldst indeed have known it; Thou knowest what is in my mind, and I do not know what is in Thy mind, surely Thou art the great Knower of the unseen things. (Qur'an 5:116)

This threesome has never been affirmed as the divine Trinity by any branch of Christianity before, during or after Muhammad. The Qur'an is simply wrong on this and thus should not be taken seriously on this issue. The Muslim, however, may press the purely logical point that God cannot be three and one (although the Qur'an does not do so). To this we respond in the same spirit and with the same logic as when the incarnation is rejected as illogical. The orthodox formulation of the doctrine is not that of a contradiction, and there are various ways of understanding God's oneness and God's triunity without contradiction. The backbone of any approach is to argue that God is one in one respect (the divine essence of substance) and three in another respect (the personhood of each member).

Douglas Groothuis. Christian Apologetics: A Comprehensive Case for Biblical Faith (pp 608-609)