Muslims consider Jews and Christians to be “People of the Book” because they believe that the Jewish and Christian scriptures were inspired by God in much the same way that the Koran was. They honor the Jewish and Christian prophets and consider them to be important prophets in Islam as well. For this reason, they believe that the Jews and the Christians are part of the same religious tradition that Muslims belong to.
Muslims believe that the Jewish prophets and Jesus were all divinely inspired. They accept that Jews and Christians are monotheistic and that the God that all three religions worship is the same God. They believe that God first revealed himself to Abraham. This made Abraham the first Muslim. While Muslims do respect Jews and Christians as People of the Book, they also believe that these faiths have drifted away from God’s true word. They believe that the older religions became imperfect and that God revealed himself (through his angel) to Muhammad to get people back on the right track. They believe that Muhammad was God’s final prophet and that the revelations given to him are the ultimate indicators of what God wants.
Muslims, then, believe that Jews and Christians are “People of the Book” because they are all part of the same religious tradition with and they all revere the same God. The scriptures that the Jews and Christians believe in are also holy to Muslims, but Muslims believe that the revelations given to Muhammad and written down in the Koran supersede and perfect the Jewish and Christian scriptures.
jews werebthe followers of hazrat Daud(David) and Christians followed Hazrat Issa(jesus) both were the respectable holy prophets sent by Allah Almighty and they had recieved holy scripts such as, Zaboor and Anjeel(Bible). so is the case with muslims as they are benefited by the holy Quran. hence we, jews, and christians are Ahle-kitaab or 'People of book'. In Quran Allah has called them as Ahle-Kitaab.
"The People of the Book" is actually quite simple. Many people do not understand that Judaism is the precursor to Christianity. They believe in the same God and have the same founding fathers and, ultimately, the same foundations. Jesus, the "founder" of Christianity, was himself a Jewish rabbi. This shared founding is seen in their holy books. The Jewish Holy Book is known as the Torah. The Christian Holy Book is much longer, and is The Bible. The Bible is split into 2 parts: The Old Testament & The New Testaments. The Torah actually appears in The Bible in the Old Testament. Genesis, Exodus, Leviticus, Numbers, and Deuteronomy are all part of both Holy Books and are also known as the Pentateuch.
Which is why these two faiths are sometimes referred to as "the people of the book," as they essentially share one.
Because that is the way in which it is mentioned in the Muslim scripture, the Quran. Moreover, the Muslims believe that there were books( Torah and Injeel) divinely revealed to the previous nations of the Jews and the Christians .
Muslims believes that the major Abrahamic religions (Judaism, Christianity, and Islam) are God's message to all humanity and the divine guidance to his way. Both Christianity and Judaism prophets were given a book with teaching for their followers, thus considered "people of the books". Furthermore, The book that were mentioned in the holy Quran are :
1. The scriptures of Abraham (Ibrahim).
2. The Torah, revealed to Moses (Mosa).
3. The Psalms revealed to David (Dawud).
4. The Gospel (Injeel) revealed to Jesus (Issa).
5. The Pages (scripture) revealed to Moses (Moosa), though some of the interpreters of the Qur'an said that the pages of Moses are in Torah.
6. The Qur'an, reveled to Muhammad.
Because they follow the old books of the prophets .