Short answer
Yes. The Qur'an gives his own words from the cradle. He says God (﷾) "hath made me kind to my mother". He spoke them to defend Mary, when her people accused her after his birth. The Qur'an honours her too. It says God (﷾) chose her, purified her, and chose her above the women of all nations. Matthew tells a different scene. His mother and brothers came to speak with him. He answers, "Who is my mother?", and points to his disciples instead. Muslims measure such scenes by the Qur'an, and do not accept that a prophet of God (﷾) turned away from the woman God (﷾) chose. The Jesus of the Qur'an is the dutiful son. The Muslim who cares for his mother in her old age follows him.
Full explanation
His first words defend his mother
The Qur'an tells how Mary brought the newborn Jesus to her people. They accused her of wrongdoing. She pointed to the child, and he spoke from the cradle. He said he was a servant of Allah (﷾) and a prophet, and that God (﷾) had made him kind to his mother. The Arabic words barran bi-walidati mean kind, dutiful and devoted to her.
“"O sister of Aaron! Thy father was not a man of evil, nor thy mother a woman unchaste!"”
“But she pointed to the babe. They said: "How can we talk to one who is a child in the cradle?"”
“He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet;”
“"(He) hath made me kind to my mother, and not overbearing or miserable;”
How the Qur'an honours Mary
The Qur'an says God (﷾) chose Mary, purified her and chose her above the women of all nations. It calls her a woman of truth. A whole chapter of the Qur'an bears her name.
“Behold! the angels said: "O Mary! Allah hath chosen thee and purified thee- chosen thee above the women of all nations.”
“Christ the son of Mary was no more than a messenger; many were the messengers that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth make His signs clear to them; yet see in what ways they are deluded away from the truth!”
The scene in Matthew and Mark
Matthew and Mark tell the same story. His mother and brothers stand outside and ask to speak with him. He answers with a question, "Who is my mother?", and names the people around him as his family instead. Christians take the last verse as the point: whoever does God's (﷾) will belongs to his family.
“While he yet talked to the people, behold, his mother and his brethren stood without, desiring to speak with him. Then one said unto him, Behold, thy mother and thy brethren stand without, desiring to speak with thee. But he answered and said unto him that told him, Who is my mother? and who are my brethren? And he stretched forth his hand toward his disciples, and said, Behold my mother and my brethren! For whosoever shall do the will of my Father which is in heaven, the same is my brother, and sister, and mother.”
“And he answered them, saying, Who is my mother, or my brethren? And he looked round about on them which sat about him, and said, Behold my mother and my brethren! For whosoever shall do the will of God, the same is my brother, and my sister, and mother.”
What a son owes his mother in Islam
The Qur'an puts kindness to parents in the same sentence as the worship of God (﷾). It forbids even a word of contempt to them in their old age. It reminds a man of what his mother bore for him. The Prophet (ﷺ) placed being dutiful to parents next after prayer at its proper time. He also named the mother three times before the father.
“Thy Lord hath decreed that ye worship none but Him, and that ye be kind to parents. Whether one or both of them attain old age in thy life, say not to them a word of contempt, nor repel them, but address them in terms of honour. And, out of kindness, lower to them the wing of humility, and say: "My Lord! bestow on them thy Mercy even as they cherished me in childhood."”
“And We have enjoined on man (to be good) to his parents: in travail upon travail did his mother bear him, and in years twain was his weaning: (hear the command), "Show gratitude to Me and to thy parents: to Me is (thy final) Goal.”
Abdullah ibn Mas'ud asked the Prophet (ﷺ) which deed Allah loves most. He said: the prayer offered at its proper time. Asked what comes next, he said: being good and dutiful to one's parents.
Abu Huraira reports that a man asked the Prophet (ﷺ) who most deserves his good company. The Prophet said: your mother. The man asked three more times who came next, and the answer was your mother, then your mother, and then your father.
Verse by verse
Luke 2:51 — Gospel of Luke, chapter 2, verse 51
“And he went down with them, and came to Nazareth, and was subject unto them: but his mother kept all these sayings in her heart.”
Cited for
Luke says he was subject to his parents, so the Gospels show an obedient son.
The response
Muslims agree he was a dutiful son. That is what the Qur'an says of him from the cradle. What Muslims reject is Matthew's scene, where the same son answers "Who is my mother?" while she waits outside.
Where it lands — Luke's verse agrees with the Qur'an's picture. It is Matthew's scene that does not.
Matthew 12:46-50 — Gospel of Matthew, chapter 12, verses 46-50
“While he yet talked to the people, behold, his mother and his brethren stood without, desiring to speak with him. Then one said unto him, Behold, thy mother and thy brethren stand without, desiring to speak with thee. But he answered and said unto him that told him, Who is my mother? and who are my brethren? And he stretched forth his hand toward his disciples, and said, Behold my mother and my brethren! For whosoever shall do the will of my Father which is in heaven, the same is my brother, and sister, and mother.”
Cited for
Christians read this as a lesson, not a snub: obedience to God makes a family closer than blood, and Mary herself did God's will.
The response
The Qur'an joins the two in one sentence: worship none but Him, and be kind to parents. Even parents who urge a son to worship others must be kept company with justice. The Jesus of the Qur'an says he is God's (﷾) servant and, in the next breath, that God (﷾) made him kind to his mother. A lesson about God's (﷾) family did not need him to answer "Who is my mother?" while she waited outside. Nor did it need him to point to others instead.
Where it lands — Even on the Christian reading, the scene sets his mother aside to make a point. The Qur'an joins duty to God (﷾) and kindness to one's mother, and that is the Jesus Muslims follow.
John 19:26-27 — Gospel of John, chapter 19, verses 26-27
“When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son! Then saith he to the disciple, Behold thy mother! And from that hour that disciple took her unto his own home.”
Cited for
From the cross Jesus made sure his mother would be cared for, which shows a loving son.
The response
The Qur'an says he was not killed or crucified, so it does not accept this scene at the cross. It needs no such scene to show his love for Mary. In the Qur'an he says, from the day he was born, that God (﷾) made him kind to his mother.
Where it lands — The Qur'an's picture of the dutiful son does not rest on the crucifixion, which it denies. It rests on his own words from the cradle.
Perspectives
Mainstream Christian
Jesus honoured his mother. In Matthew 12 he teaches that obedience to God makes a family, not that Mary means nothing to him. John tells that, on the cross, he gave her into the care of the disciple he loved.
Matthew 12:50 says whoever does the will of the Father is his brother, sister and mother. Christians read this as widening his family, not rejecting Mary.
Rebuttal
Islam too puts God (﷾) first. Yet even toward parents who urge a son to worship others, the Qur'an says, "bear them company in this life with justice". A lesson about God's (﷾) family did not need him to answer "Who is my mother?" while she waited outside.
John records Jesus giving his mother into the care of the beloved disciple from the cross.
Rebuttal
Caring for a mother is dutiful, and Islam agrees. But the Qur'an says he was not killed or crucified, so it does not accept this scene. It needs no such scene: it has him say, from the cradle, that God (﷾) made him kind to his mother.
Luke says the boy Jesus went home to Nazareth with his parents and "was subject unto them".
Rebuttal
Islam agrees that he was an obedient son, as the Qur'an says of him from the cradle. Luke's verse fits the Qur'an's picture. It is Matthew's scene, with "Who is my mother?", that does not.
The Islamic perspective
Jesus was the dutiful son of a mother God (﷾) chose and purified. The Prophet (ﷺ) taught Muslims to honour their mothers in the same way.
The Qur'an records Jesus saying from the cradle that God (﷾) made him kind to his mother and not overbearing.
His first words were spoken to clear his mother of her people's charge.
The Qur'an says God (﷾) chose Mary, purified her and chose her above the women of all nations.
In Matthew, his mother came to speak with him. Jesus answered "Who is my mother?" and pointed to his disciples instead.
Mark tells the same scene in almost the same words.
The Qur'an joins kindness to parents to the worship of God (﷾). It forbids a word of contempt to them in old age.
The Prophet (ﷺ) ranked being dutiful to parents next after prayer at its proper time.
The Prophet (ﷺ) was asked who most deserves a person's good company. He named the mother three times before the father.