Islam teaches that God is absolutely One. For Muslims, to say that God is three persons, or that He has a son, takes away from His oneness and makes something else equal to Him.
The fuller answer
The Quran does not insult Christians. It asks them respectfully to come to a common word: that we worship none but God. It says that Jesus, like Adam, was created by God's word, and that the Messiah, son of Mary, was only a messenger. The Quran says: 'Do not say three. Stop, it is better for you.'
Muslims note that Jesus himself taught 'The Lord our God, the Lord is one', and that the word 'Trinity' does not appear in the Gospels. Christians answer that the Trinity is a mystery about one God in three persons. Muslims respect that they disagree, and keep to the simple oneness that the Quran teaches.
O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs.
They have certainly disbelieved who say, "Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.
Say, "O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allah and not associate anything with Him and not take one another as lords instead of Allah." But if they turn away, then say, "Bear witness that we are Muslims [submitting to Him]."
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.
