And the Jews say: Ezra is the son of Allah, and the Christians say: The Messiah is the son of Allah. That is their saying with their mouths. They imitate the saying of those who disbelieved of old. Allah (Himself) fighteth against them. How perverse are they! They have taken as lords beside Allah their rabbis and their monks and the Messiah son of Mary, when they were bidden to worship only One Allah. There is no Allah save Him. Be He Glorified from all that they ascribe as partner (unto Him)! Surah 9:30-31

The Koran warns against making people, like Ezra and Jesus, into gods. It believes if you make Jesus the son of Allah, then you make two gods, which if forbidden.

Muhammad does explore the possibility of God having a Son.

Say: “If (Allah) Most Gracious had a son, I would be the first to worship.” Surah 43:81

Muhammad told his followers: If Allah had a son, then he must be worshipped. But, it says, if God had a son, it would not be fitting.

It is not befitting to (the majesty of) Allah that He should beget a son. Glory be to Him! when He determines a matter, He only says to it, “Be”, and it is. Surah 19:35

It’s not stated why that would be unfitting. One possible reason is the idea of Allah having sex to produce a child.

The Originator of the heavens and the earth! How can He have a child, when there is for Him no consort, when He created all things and is Aware of all things? Surah 6:101

While the Koran cannot fathom God having sex, it promotes a heaven where men will have sex with virgins.
However, the Koran believes Mary was impregnated by the Holy Spirit, not by a sexual act, to produce Jesus, which is exactly what the Bible believes.

And Mary, daughter of ‘Imran, whose body was chaste, therefore We breathed therein something of Our Spirit. And she put faith in the words of her Lord and His scriptures, and was of the obedient. Surah 66:12

If Allah impregnated Mary with his spirit, couldn’t he call that his son? Isn’t it technically a child that part man/part spirit? Why is that so different from Christianity and hard to believe?

They say: “((Allah)) Most Gracious has begotten a son!” Indeed ye have put forth a thing most monstrous! At it the skies are ready to burst, the earth to split asunder, and the mountains to fall down in utter ruin, That they should invoke a son for ((Allah)) Most Gracious. For it is not consonant with the majesty of ((Allah)) Most Gracious that He should beget a son. Not one of the beings in the heavens and the earth but must come to ((Allah)) Most Gracious as a servant. Surah 19:88-93

The Koran, apparently, dismisses the claim Allah had a son, believing it would below the majesty of Allah to do such a thing, and says Muslims have no knowledge of it.

Further, that He may warn those (also) who say, “Allah hath begotten a son”: No knowledge have they of such a thing, nor had their fathers. It is a grievous thing that issues from their mouths as a saying what they say is nothing but falsehood! Surah 18:4-5

The Bible claims that it does have knowledge that Jesus is the son of God and it comes directly from God himself.

During his baptism. . .

As soon as Jesus was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and lighting on him. And a voice from heaven said, “This is my Son, whom I love; with him I am well pleased.” Matthew 3:16-17

During a moment on the mountain with his disciples...

While he was still speaking, a bright cloud enveloped them, and a voice from the cloud said, “This is my Son, whom I love; with him I am well pleased. Listen to him!” When the disciples heard this, they fell facedown to the ground, terrified. Matthew 17:5-6