1) Our Muslim friend alleges that the Bible is wrong, because the Bible says that God repented.
2) But, the Koran (at 2:37) teaches that Allah repented.
3) Therefore, if our Muslim friend is to be consistent, he would have to say that the Koran is wrong.
The video alleges that the Koran, at 2:37, does not say that Allah repented. The Online Quran Project provides a number of English translations. Here are the translations I found there of that particular ayah of surah 2.
Abul Ala MaududiFor the purists, the Arabic is this:37. At that time Adam learnt appropriate words from his Lord and repented, and his Lord accepted his repentance, for He is very Relenting and very Merciful.
Abdullah Yusuf Ali
37. Then learnt Adam from his Lord words of inspiration, and his Lord Turned towards him; for He is Oft-Returning, Most Merciful.
Ali Quli Qara'i
37. Then Adam received certain words from his Lord, and He turned to him clemently. Indeed He is the All-clement, the All-merciful.
Arthur John Arberry
37. Thereafter Adam received certain words from his Lord, and He turned towards him; truly He turns, and is All-compassionate.Wahiduddin KhanAhmed Ali
37. Then his Lord sent commands to Adam and turned towards him: Indeed He is compassionate and kind.
37. Then Adam received some words from his Lord and He turned towards him. He is the Ever-Returning, the Most Merciful.
37. (Aware of his lapse and in the hope of retrieving his error, rather than attempting to find excuses for it,) Adam received from his Lord words that he perceived to be inspired in him (because of his remorse, and he pleaded through them for God’s forgiveness). In return, He accepted his repentance. He is the One Who accepts repentance and returns it with liberal forgiveness and additional reward, the All-Compassionate (especially towards His believing servants).
Amatul Rahman Omar
37. After that Adam received from his Lord certain (useful) commandments and He turned to him with mercy. He, indeed is Oft-returning with compassion, the Ever Merciful.George Sale
37. [Out of mercy] Adam received from his Lord some words of supplication. [Once he returned to his Lord with those words of supplication,] God forgave Adam as He is the most forgiving and merciful.Abdul Majid Daryabadi
37. Then Adam learnt from his Lord certain Words, and He relented toward him, verily He! He is the Relentant, the Merciful.
Edward Henry Palmer
37. And Adam caught certain words from his Lord, and He turned towards him, for He is the compassionate one easily turned.
37. Then Adam learnt from his Lord certain words (of revelation), therefore Allah accepted his repentance; indeed He only is the Most Acceptor of Repentance, the Most Merciful.
37. And Adam learned words of prayer from his Lord, and God turned unto him, for He is easy to be reconciled and merciful.Hamid S. Aziz
37. And Adam obtained certain words (revelations) from his Lord, and He relented towards him, for He is the Relenting, the Compassionate.Mahdi Pooya
37. not yet included, see Chapter 90-114
Muhammad Taqi-ud-Din al-Hilali & Muhammad Muhsin Khan
37. Then Adam received from his Lord Words. And his Lord pardoned him (accepted his repentance). Verily, He is the One Who forgives (accepts repentance), the Most Merciful.
John Medows Rodwell
37. And words of prayer learned Adam from his Lord: and God turned to him; for He loveth to turn, the Merciful.
Muhammad Ahmed & Samira
37. So Adam received from his Lord words/expressions, so (He) forgave on him, that He is, He is the forgiver , the most merciful .Muhammad Aqib Farid Qadri
37. Then Adam learnt from his Lord certain words (of revelation), therefore Allah accepted his repentance; indeed He only is the Most Acceptor of Repentance, the Most Merciful. (See Verse 7:23)Muhammad Asad
37. Thereupon Adam received words [of guidance] from his Sustainer, and He accepted his repentance: for, verily, He alone is the Acceptor of Repentance, the Dispenser of Grace.
Muhammad Mahmoud Ghali
37. Then Adam received (some) Words from his Lord; so He relented towards him; surely He, Ever He, is The Superbly Relenting, The Ever-Merciful.
37. Adam was inspired by some words (of prayer) through which he received forgiveness from his Lord, for He is All-forgiving and All-merciful.
Muhammad Taqi Usmani
37. Then ‘Adam learned certain words (to pray with) from his Lord; so, Allah accepted his repentance. No doubt, He is the Most-Relenting, the Very-Merciful.Maulana Muhammad Ali
37. Then Adam received (revealed) words from his Lord, and He turned to him (mercifully). Surely He is Oft-returning (to mercy), the Merciful.
Muhammad Marmaduke Pickthall
37. Then Adam received from his Lord words (of revelation), and He relented toward him. Lo! He is the relenting, the Merciful.
Hasan Al-Fatih Qaribullah & Ahmad Darwish
37. Then Adam received Words from his Lord, and his Lord relented towards him. He is the Receiver of Repentance, the Merciful.
37. Then, Adam received from his Lord words, whereby He redeemed him. He is the Redeemer, Most Merciful.
37. (The solution to this catastrophe was beyond human intellect.) Then Adam received Words of guidance from his Lord and He accepted his repentance. Behold, He is the Acceptor, the Most Merciful. (Adam = Man. His wife = Woman. She also repented and Allah treated both of them equally (7:23-24))Shakir
37. Then Adam received (some) words from his Lord, so He turned to him mercifully; surely He is Oft-returning (to mercy), the Merciful.Syed Vickar Ahamed
37. Then Adam received the words of inspiration, from his Lord, and his Lord forgave him; For He is One Who accepts Repentance (Tawwab), Most Merciful (Raheem).Tahir al-Qadri
37. Then Adam learnt some words (of humility and repentance) from his Lord. So Allah accepted his repentance. Surely He is the One Who is Most Relenting, Ever-Merciful.T. B. Irving
37. Adam received words [of inspiration] from his Lord and he turned towards Him. He is the Relenting, the Merciful!"Umm Muhammad (Sahih International)
37. Then Adam received from his Lord [some] words, and He accepted his repentance. Indeed, it is He who is the Accepting of repentance, the Merciful.37. Then Adam received some words [of prayer] from his Lord and He accepted his repentance. He is the Forgiving One, the Merciful.
37. Prompted by the sense of guilt, Adam felt shame, but because guilt did not reside in the intention, Allah in mercy inspired him with a prayer for invoking His forgiveness, and in turn did Allah give up resentment against him and pardon his offence: it is He Who always accepts true repentance and the atonement made by the people, He is AL-Rahim.[Progressive Muslims]
37. Adam then received words from His Lord, so He forgave him; He is the Forgiver, the Merciful.
37 فَتَلَقَّىٰٓ ءَادَمُ مِن رَّبِّهِۦ كَلِمَتٍۢ فَتَابَ عَلَيْهِ ۚ إِنَّهُۥ هُوَ ٱلتَّوَّابُ ٱلرَّحِيمُ
Note that, of course, not all of the translations are equally literal or equally authoritative. The purpose in presenting them all is two-fold. First, I want to affirm that none of them (not one!) says "Allah repents." Not one uses those exact words. On the other hand, many of them identify Allah as "oft-returning" or "oft-turning" or the like, which has the same sense. Obviously, some take a different tack completely. The point, though, is that there is a reasonable basis for the idea that Allah "turns" whether one uses the word "repent" or not.
That reason is the reason given by Paul Rezkella in the comments section of the post where I found the video:
If you read the arabic in Surah 2:37, you read the word “tawwabu”, which means “repenting”. “…and his Lord repented (fataba) towards him; for He is Oft-Repenting (huwa al-tawwabu), Most Merciful.” S. 2:37Of course, Sam Shamoun has already written about this. He points out that there at least four more such places. Also Sam Shamoun has already explained about the idea in the Bible of God repenting, with comparisons to the Koran.
But the fundamental error of the person in the video seems to be his assumption that if the term "repenting" is not used by the translators, the sense of the word is not there. That's a mistaken argument.
Of course, there's a possible alternative error. Some poor deluded person might think that when the KJV says that God "repented," they mean that God turned from sins. Such a notion would be the result of someone simply not understanding English very well. That would be excusable in the case of someone who is not a native English speaker, as perhaps may be the case for the person in the video. But such a notion is completely wrong and unfounded.
In any event, someone who wants a more thorough, detailed discussion can peruse Sam Shamoun's articles at the links above.