My post is not intended to offend christians, but merely to academically discuss issues with them in a manner i hope is equitible and polite, as the Quran says "Invite all to the way of your lord through wisdom and beautiful preaching, and argue with them in ways that are best.."
It would be a strawman to argue that muslims are against the idea of a triune God simply because the Quran says so. The Quran in several occasions expands upon the oneness of God also.
Why muslims are against the 'trinity'.
1. God is not numerical, has no form, can not be divided or undergo change. God being one means in his essence, there can only be 'God'. Something must exist by necessity of it's own existence, or nothing would exist. Material existence is contingent, and there are a plethora of arguments for a immaterial creator not confined to space, limitations, or contingencies. The creator therefore can not quantified by two or three, and therefore is 'one' by the meaning the 'only one'. Can a transcendent, immaterial reality also be a corporal, contingent, physical one? Can God create a rock he can't lift? Can God not become God, are all contradictory baseless questions.
2. IF God can be confined to a body he ceases to be God by the very arguments that we used to prove his existence.
3. The idea of Jesus coming to die for our sins was invented. Therefore what was also invented was he must be God or part of God somehow, because only such a great status is enough to absolve for our sins. Islam rejects such a concept. We are all liable for our sins, the Quran tells us that no soul shall bear the burden of another. No-one has died for our sins. With the facets of intelligence, of our own choice and deduction do we pave the path to our own ultimate destiny. Despite this, we will all be , If God wills, judged by the mercy of God, who we declare his mercy daily several times.
4. Even in the Bible, do you see Jesus pbuh preaching monotheism - even though the bible in itself is corrupted:
The most important commandment in the entire Bible is that God is not trinity, but one in unique oness.
"The most important one," answered Jesus, "is this: 'Hear, O Israel: The Lord our God, the Lord is one". Bible
The 'Son of God' title is given to other prophets of God too.
In Exodus 4:22 "Thus saith Jehovah, Israel is my son, even my firstborn." Israel was called God's First Son.
In Jeremiah 31:9 "I am a father to Israel, and Ephraim is my firstborn."Ephraim is God's First Son and First Born.
In Psalm 2:7 "....Jehovah had said onto me (David), thou art my Son; this day have I begotten thee." David was called God's Begotten Son.
There is no place where Jesus pbuh himself to my knowledge uses the word trinity.
You see traces of pure monotheism in the Bible, with corruption ofcourse.
I will leave you with these hadiths:
Al Kafi
H 313, Ch. 16, h 4 – Graded Sahih by Alama Majlisi
The Imam said, "There is nothing in the universe, but that is subject to annihilation, alteration, change, decay, transition from one color to another, from one shape to another and from one quality to another. They increase, decrease and change from decrease to increase, except He, Who is the Lord of the worlds. He alone is eternal and in one state. He is the first, before every thing and the last eternally.His attributes and names do not change as they do in the case of others. A man at one time is dust, at other time flesh and blood, then turns into decaying bones and finally becomes dust. A piece of date at one time is raw, at another time ripe, mature and then it dries up. With every change, the names and attributes also change. Allah, the Majestic, the Glorious is different from all such things."
Al Kafi:
Graded Muwathaq
He said: I said to Abu `Abdillah عليه السلام: I heard Hisham b. al-Hakam narrate from you that Allah has a body, supported by light, His recognition is necessary and He bestows this [knowledge] upon whom He wills from the creation. So he عليه السلام said: Glorified be He, whom no one knows how He is except Himself. There is nothing like unto Him, and He is the Hearing, the Seeing. He cannot be limited, nor can He be felt, nor can He be moved, nor can He be comprehended [by sight, nor by] the senses, nor can He be contained in anything, nor does He have a body, nor does He have a form, nor a figure, nor a confine. (al-Kafi, Volume 1, hadith 278)