Allāh, the Most High said:

وَقَالَتِ الْيَهُودُ عُزَيْرٌ ابْنُ اللَّهِ وَقَالَتِ النَّصَارَى الْمَسِيحُ ابْنُ اللَّهِ ۖ ذَٰلِكَ قَوْلُهُم بِأَفْوَاهِهِمْ ۖ يُضَاهِئُونَ قَوْلَ الَّذِينَ كَفَرُوا مِن قَبْلُ ۚ قَاتَلَهُمُ اللَّهُ ۚ أَنَّىٰ يُؤْفَكُونَ ‎﴿٣٠﴾‏ اتَّخَذُوا أَحْبَارَهُمْ وَرُهْبَانَهُمْ أَرْبَابًا مِّن دُونِ اللَّهِ وَالْمَسِيحَ ابْنَ مَرْيَمَ وَمَا أُمِرُوا إِلَّا لِيَعْبُدُوا إِلَٰهًا وَاحِدًا ۖ لَّا إِلَٰهَ إِلَّا هُوَ ۚ سُبْحَانَهُ عَمَّا يُشْرِكُونَ ‎﴿٣١﴾‏
يُرِيدُونَ أَن يُطْفِئُوا نُورَ اللَّهِ بِأَفْوَاهِهِمْ وَيَأْبَى اللَّهُ إِلَّا أَن يُتِمَّ نُورَهُ وَلَوْ كَرِهَ الْكَافِرُونَ ‎﴿٣٢﴾‏

And the Jews said: ‘ʿUzayr (Ezra) is the son of Allāh’, and the Christians said: ‘The Messiah is the son of Allāh’. That is their statement from their mouths. They imitate the saying of those who disbelieved before (them). May Allāh curse them, how they are deluded (from truth to lies)! They have taken their scholars and monks as lords besides Allāh, and [also] the Messiah, the son of Mary. And they were not commanded except to worship one God; there is no deity [worthy of worship] except Him. Exalted is He above whatever they associate with Him. They want to extinguish the light of Allāh with their mouths, but Allāh refuses except to perfect His light, although the disbelievers dislike it.
[Al-Tawbah, 9:30-32]

Shaykh al-Islām Ibn Taymiyyah (d. 728 AH) explains:

These are evidence(s) that clearly show that he (صلى الله عليه وسلم) was raised as a messenger of Allāh sent to the Christians and the rest of the People of the Book. [It proves] that he called them [to Islām] and struggled against them [with evidence, debate, and war for those inciting it] and ordered others to invite [the People of the Book to Islām] and struggle against them [in this way]. [This invitation] is not an innovation started by those who came after him (صلى الله عليه وسلم). Like the innovations perpetrated by the Christians after the Messiah (peace be upon him) [ascended].

For, indeed, the Muslims do not allow anyone after Muḥammad (صلى الله عليه وسلم) to change a single law in their legislation [sharīʿah]. They do not make permissible [ḥalāl] what has been made unlawful [ḥarām], nor do they make unlawful [ḥarām] that which has already been made lawful [ḥalāl]. They do not obligate that which has been abrogated, nor do they abrogate that which has been obligated. Rather, according to them, that which is lawful is only that which Allāh and His Messenger (صلى الله عليه وسلم) have made lawful, and what is impermissible is only that which has been made impermissible by Allāh and His Messenger. This religion is only what has been legislated by Allāh and His Messenger.

This is in strong contrast to the Christians who have innovated matters after [the ascension of] the Messiah (peace be upon him). He never legislated these innovative matters for them, nor did any of their bibles, nor did any of the prophetic books that came before them. Rather, they claim that their leaders have legislated these religious innovations and that the Messiah (peace be upon him) wholeheartedly endorses them. This is the point [of contention] of which the companions of the three religions have argued: the Muslims, the [modern-day] Christians, and the [modern-day] Jews. Just as they have argued regarding the Messiah (peace be upon him) and other issues.

As for the Jews: they do not allow Allāh–the Exalted, the Most High–to abrogate anything that He has legislated.

As for the Christians: they allow their leaders to abrogate the legislations of Allāh in light of their own opinions and views.

As for the Muslims: they believe that to Allāh alone belongs the creation and its order [in entirety]. There exists no legislation except that which has been instated upon the tongues of the messengers. It is for Him alone to abrogate whatever He wills just as Allāh abrogated through his raising of the Messiah [some] of the legislations of the Prophets who came before him.

Source: Al-Jawāb al-Saḥīḥ: 340-1
Translated by: Riyāḍ al-Kanadī