For those who would like to take a closer look at the Qur'an verses on abrogation, here are 2:106 and 16:101, along with three Muslim commentaries on these verses.
Surah 2:106—“Whatever communications We abrogate or cause to be forgotten, We bring one better than it or like it. Do you not know that Allah has power over all things?”
Tafsir al-Jalalayn on 2:106—When the disbelievers began to deride the matter of abrogation, saying that one day Muhammad enjoins his Companions to one thing and then the next day he forbids it, God revealed: And whatever verse (mā is the conditional particle), that has been revealed containing a judgement, We abrogate, either together with its recital or not [that is only its judgement, but its recital continues]; there is a variant reading, nunsikh, meaning ‘[Whatever verse] We command you or Gabriel to abrogate’, or postpone, so that We do not reveal the judgement contained in it, and We withhold its recital or retain it in the Preserved Tablet; a variant reading [of nunsi’hā] is nunsihā, from ‘to forget’: so ‘[Whatever verse We abrogate] or We make you forget, that is, We erase from your heart’; the response to the conditional sentence [begun with mā] is: We bring [in place] a better, one that is more beneficial for [Our] servants, either because it is easier [to implement] or contains much reward; or the like of it, in terms of religious obligation and reward; do you not know that God has power over all things?, including abrogating and substituting [verses]? (the interrogative here is meant as an affirmative).Surah 16:101—“And when We change (one) communication for (another) communication, and Allah knows best what He reveals, they say: You are only a forger. Nay, most of them do not know.”
Tafsir Ibn Abbas on 16:101—Then Allah mentions what was abrogated of the Qur’an and that which was not abrogated, as a direct reference to the claim of the Quraysh who said to the Prophet: O Muhammad! Why do you command us to do something and then forbid it, saying: (Such of Our revelations as We abrogate) We do not erase a verse that was acted upon before and which is now not acted upon (or cause to be forgotten) or leave unabrogated so that it is acted upon, (We bring one better) We send Gabriel with that which more profitable and easier to act upon (or the like) in reward, benefit and action. (Knowest thou not) O Muhammad (that Allah is Able to do all things?) of the abrogated and unabrogated.
Al-Wahidi on 16:101—(Nothing of our revelation (even a single verse) do we abrogate or cause be forgotten, but we bring (in place) one better or the like thereof) [2:106]. The commentators of the Qur’an said: “The idolaters said: ‘Do you not see that Muhammad commands his Companions with something and then forbids them from the same and commands them to the exact opposite. One day he says something and the following day he retracts it. This Qur’an is nothing but the speech of Muhammad who has invented it. It is a speech that contradicts itself’. Allah, exalted is He, therefore revealed this verse (And when We put a revelation in place of (another)…) [16:101] and also (Nothing of our revelation (even a single verse) do we abrogate or cause be forgotten, but we bring (in place) one better or the like thereof…)”.
Tafsir al-Jalalayn on 16:101—And when We exchange a verse in place of a [different] verse, by abrogating it and revealing another, for the welfare of [God’s] servants — and God knows best what He reveals — they say, that is, the disbelievers [say] to the Prophet (s): ‘You are just a fabricator’, a liar, making it up yourself. Nay, most of them do not know, the true nature of the Qur’ān and the benefit [to God’s servants] of abrogation.For more on the doctrine of abrogation, see:
Tafsir Ibn Abbas on 16:101—(And when We put a revelation) when We send Gabriel with an abrogating verse (in place of (another) revelation) in place of another abrogated verse, (and Allah knoweth best what He revealeth) and Allah knows the probity of that with which He commands His servants, (they say) the disbelievers of Mecca say: (Lo! thou art but inventing) from yourself, O Muhammad. (Most of them know not) that Allah commands His servants with that which is good for them.
Al-Wahidi on 16:101—(And when We put a revelation in place of (another) revelation…) [16:101-102]. This verse was revealed when the idolaters said: “Muhammad is mocking his Companions; one day he commands them to do something and the next day he forbids them from doing it, or brings instead something which is easier. He is nothing but a calumniator who says things of his own invention”, and so Allah, exalted is He, revealed this verse and the verse after it.
Farooq Ibrahim, "The Problem of Abrogation in the Quran"
Robert Spencer, "The Islamic Doctrine of Abrogation"
Sam Shamoun, "Abrogated Verses of the Quran: Evidence from Islamic Sources"