Why does Islam reject the current versions of the Bible and Torah, even though the Qur'an confirms the existence of previous Christian and Jewish prophets like Abraham, Moses and Jesus in the Qur'an?
The Torah and Gospel were originally from Allah, may He be exalted, and Muslims are obliged to believe in them, because Allah, may He be exalted, says (interpretation of the meaning):
“Say (O Muslims), ‘We believe in Allah and that which has been sent down to us and that which has been sent down to Ibraaheem (Abraham), Ismaa‘eel (Ishmael), Ishaaq (Isaac), Ya‘qoob (Jacob), and to Al-Asbaat (the twelve sons of Ya‘qoob (Jacob)), and that which has been given to Moosa (Moses) and ‘Eesa (Jesus), and that which has been given to the Prophets from their Lord. We make no distinction between any of them, and to Him we have submitted (in Islam)’”
“O you who believe! Believe in Allah, and His Messenger (Muhammad (blessings and peace of Allah be upon him)), and the Book (the Quran)which He has sent down to His Messenger, and the Scripture which He sent down to those before (him), and whosoever disbelieves in Allah, His Angels, His Books, His Messengers, and the Last Day, then indeed he has strayed far away”
But the Torah and Gospel were subjected to distortion and changes. We may categorize the statements in Qur'an about those two holly books - regarding their credibility - into these categories:
Verses that state the happening of distortion generally without mentioning the extent of that distortion nor its forms. Of these verses Allah, may He be exalted, says (interpretation of the meaning):
"Do you (faithful believers) covet that they will believe in your religion inspite of the fact that a party of them (Jewish rabbis) used to hear the Word of Allah [the Taurat (Torah)], then they used to change it knowingly after they understood it?"
and about the Children of Israel (Jews) (interpretation of the meaning):
"So because of their breach of their covenant, We cursed them, and made their hearts grow hard. They change the words from their (right) places and have abandoned a good part of the Message that was sent to them..."
Explicit verses stating that Jewish rabbis concealed some of their sent-down books and hid some of their facts. Allah, may He be exalted, says (interpretation of the meaning):
"Say (O Muhammad ): "Who then sent down the Book which Musa (Moses) brought, a light and a guidance to mankind which you (the Jews) have made into (separate) papersheets, disclosing (some of it) and concealing (much)..."
"Those to whom We gave the Scripture (Jews and Christians) recognise him (Muhammad or the Ka'bah at Makkah) as they recongise their sons. But verily, a party of them conceal the truth while they know it - [i.e. the qualities of Muhammad which are written in the Taurat (Torah) and the Injeel (Gospel)]"
Verses explicitly state the happening of adding some parts that weren't originally part of these sent-down books. Allah, may He be exalted, says (interpretation of the meaning):
"And verily, among them is a party who distort the Book with their tongues (as they read), so that you may think it is from the Book, but it is not from the Book, and they say: "This is from Allah," but it is not from Allah; and they speak a lie against Allah while they know it"
“Then woe to those who write the Book with their own hands and then say, "This is from Allah," to purchase with it a little price! Woe to them for what their hands have written and woe to them for that they earn thereby”
Verses stating that some of the truth was still remaining in these books in the times of prophet Muhammad (blessings and peace of Allah be upon him). Of these verses (interpretation of the meaning):
"But how do they come to you for decision while they have the Taurat (Torah), in which is the (plain) Decision of Allah..."
"Say (O Muhammad ) "O people of the Scripture (Jews and Christians)! You have nothing (as regards guidance) till you act according to the Taurat (Torah), the Injeel (Gospel), and what has (now) been sent down to you from your Lord (the Qur'an)." Verily, that which has been sent down to you (Muhammad) from your Lord increases in many of them their obstinate rebellion and disbelief. So be not sorrowful over the people who disbelieve"
and it is stated in Qur'an that the scripture copies in the hands of the Jewish rabbis and Christians in these times had mentioned prophet Muhammad (blessings and peace of Allah be upon him) (interpretation of the meaning):
"Those who follow the Messenger, the Prophet who can neither read nor write (i.e.Muhammad ) whom they find written with them in the Taurat (Torah) and the Injeel (Gospel)..."
- translated form IslamQA with some editing
- interpretation of the meaning of Qur'an verses are quoted from the authorized Interpretation of the Meanings of The Noble Quran by Dr. Muhammad Taqi-ud-Din Al-Hilali and Dr. Muhammad Muhsin Khan
It's the Sunnah of Allah by bringing a new revelation the previous ones should be abolished, when the Qur'an came Qur'an abolished following of all previous ones because other scriptures before Qur'an they were changed and fabrications done in them and they were meant for a particular time.