Also, please read these materials if you want to more easily follow along with the commentaries I will be providing regarding the relationship between the Abrahamic faiths of Judaism, Christianity and Islam.
One of the greatest confusions about their relationship, and barrier to understanding that all three faiths are sprung from the same tree and worship the same God (both in concept and also in the reality of the historic details) is the seemingly harsh words regarding Judaism and Christianity in the Qur'an. One cannot properly understand and interpret why God allowed such things to be expressed without considering the "state of the faith" of both Judaism and Christianity at the time. Remember, God is concerned at all times with the details of the "here and now." It is humans who worry about "legacy" and "who won." Thus, God "worries" and seeks to find all the sheep to bring to his protection and love when they are alive, when they are lost, not hundreds or thousands of years in the future. In other words, God does not think to himself, "Well, I'm going to give them a faith because in a thousand years there will be a billion believers." God is always seeking to reveal his consistent truth. The same God is revealed in the holy books of the ancient Israelites, the Gospels of the Christians, and in the Qur'an. It is incorrect to take a partisan view of the sequence and time spans between these revelations. It is, after all, the very same God who is revealed within each of the three faiths.
So why did revelations occur when they did? The revelation started with first man, Adam, of course, so that is easy to understand. God sought a relationship with his creation from the beginning, and indeed, this is why humans were created at all, so that God could express his love and share his kingdom with humans. But humans are, by definition, flawed, because physical reality is so far distant from God's realm (the weakness of the flesh and mortality in contrast to the perfection of God) and also because, sadly, humans often opt to be distant from God. Thus God had to give to humans the Law and codes of conduct for their own survival, ethics and well being. This is the obvious reason for the timing of the Chosen People and the giving of the Law to the Israelites, plus God's continuing relationship with them through the ages.
The Israelites knew that they needed a Messiah, a Savior, not only because God prophesied this for them in his promise to the prophets, but also in their wisdom and discernment they recognized this need. Jews await the Messiah, while Christians proclaim that Jesus Christ was the Messiah and Savior. Thus the timing of the revelation of God for the Christians is the arrival of the Messiah and Savior, Jesus Christ. This is also easy to understand.
So why did God give a revelation to the Prophet (PBUH) many wonder. To answer this question you must remember and reflect on what I said above. God does not "wait" over the generations to reach out to humans and bring them closer to him. Thus, to understand why God chose that time and that place to bring the Arabs to him, to know him as the one true God, and to recall their roots to the patriarchs, from Adam to Abraham and the prophets, including acknowledgement and love for the message of Jesus, one needs to look at the status of Judaism and Christianity in the decades following 610 AD, the year that the angel first descended on the Prophet with a message from God.
The Prophet received the word of God, through instruction by the angel, known to be Gabriel, starting in the year 610 AD and continuing for twenty three years, to the end of his life. Thus the Qur'an was revealed and dictated in an unfolding process from the years 610-632 AD. To understand Christianity during that time, one must read the history of the Popes and the progresses and problems of their reigns. You see, the Prophet of course had no way of knowing what was going on within the faith of Christianity, only God knows all and sees all. Likewise the Jews had long ago lost their Temple, the heart of their faith, and were dispersed, and God alone knew their present and foresaw their future. God alone knows when to "wait" for humans to come to him, and when he needs to provide a push. By trusting in God's timing humans can glean some insight by looking at the facts of what the Arabs who had not yet been brought to God and who had no way of knowing, which is "what was going on in Christianity at the time?"
Think of Judaism and Christianity as the cures for mortal diseases. However, the cures are only as good as the availability to the "doctors" and their medicine. How available was Judaism and Christianity in the years from 610-632, and how "effectively" were the "cures" reaching the millions of people in the world? Judaism had been dispersed and scattered, and the Christians were still in their infancy, and in fact, I'd say the Christians were going through their "terrible two's" stage of being toddlers. And, for haters of the Roman Catholics, that has nothing to do with the Church being "invalid." The hubris and narcissism of such accusations always takes my breath away with astonishment. The Church was the sum total of the people, the Christians, all of them, so when one disrespects the ancient Catholic Church one is disrespecting your very Christian ancestors, the ordinary people, who were struggling to make the faith take root for the benefit of all. In fact, Pope Honorius I (625-638) was called Dux plebis, 'Leader of the ordinary people' because he was an active builder of churches and a continual advocate for the ordinary and average Christian. But the average and ordinary Christians were caught in the constant arguing and what we would call today "navel gazing" of the theologians, who were, believe it or not, arguing about the "true nature of Jesus Christ." Six hundred years after Jesus Christ was crucified and resurrected, the Church was embroiled in decades of debate about defining the exact nature of Jesus Christ's being.
Do you start to have a clue, now, about why God would see the need to remind people of what Jesus had constantly done, which is to point back to God, whose nature cannot be "defined?" It is one of the least attractive of humankind's faults. The Israelites, despite their many times of sin and arrogance, never, ever dared, nor would it occur to them, to try to "figure out" and "exactly define" God. Jews have, for the large part, remained true to that humility, and that is to their great credit. That is why I often say, no one "gets" (slang for comprehends) God like those Jews who retain the orthodox understanding of God. But Christians, oh Christians, what a weakness they have in this area. Part of that is because the arrogance of the pagan culture (where they make up idols and fictional gods and mythologies whenever they feel like it) of the Gentiles brought along an intellectual snobbery where they feel they can "dissect" and "define" God, particularly in the personage of Jesus Christ. Honestly, it's amazing that God "waited" six hundred years to turn to people he could trust to trust him, and not "dissect" him.
So if you want to understand why there was a revelation by God to the Prophet (PBUH), you have to be a bit of a history student, and study what was going on in the worldly events and the "status of the faith" in the reigns of Pope Boniface IV (608-15), Pope Deusdedit (later Adeodatus I) (615-618), Boniface V (619-25) and Honorious I (625-38). Again, this is not because there was something "wrong" with the Popes and, in fact, there would not be any Christianity at all today if it had not been for the keys of St. Peter being faithfully passed through many terrible times. But one cannot claim to understand Christianity, say nothing of understanding "God," if one ignores the reality of how humans, in their weakness, interacted with the kingdom of God that Jesus Christ revealed. The fact that they were arguing over the nature of Jesus Christ six hundred years later is hardly to their credit. And it was not the Popes who were to blame. In fact, Pope Honorious inadvertently took himself into heresy in an attempt to come up with a "Cliff's Notes" version of the nature of Jesus Christ, in order to simplify the complex arguments for the benefit of the suffering ordinary Christian. In trying to damp down the pointless and arrogant arguing over the "true nature" of Jesus Christ, he actually gave an oversimplified and inadvertently heretical "simple definition" to the people.
Ah ha. I can almost see those of you who have read the Qur'an now look up in comprehension and nod your heads. Do you now understand why God would have had, and human feelings and words are always inadequate when describing God, one could almost say an impatience and annoyance, expressed to the Prophet (PBUH) by the angel, with the state of Christianity, and of Judaism? That does not mean that anything in either of those God given faiths are invalid. But it means that God, in his wisdom, knew that he'd spend a lot of time sitting around and waiting for people to, if ever, sort themselves back into where they were supposed to be. God, of course, knows all and sees the future because God is the future, just as God is the past, the present and the realm that is totally outside of the existence of time. God balances free will of humans with a point where he will say "Enough!" The statement of "enough" is when God discerns that souls will be lost through humankind's delays and imperfections, NOT the imperfections of his prior message, prophets, or his Son in the form of Jesus, but in human delays and imperfections. And was God not correct? Look at the number of believers (Jews, Christians and Muslims) in the world today.
So that is the reason for the great misunderstanding that humans have brought among themselves. Instead of understanding that God knows humans and what they need far better than any human could, humans try to apply a "fault" or "supplanting" upon each other's faith, rather than understanding the context of the gift of revelation and the truth of all that has gone before.
I hope that you find this helpful. If you want to understand more about the churning that was taking place in history (Rome and Constantinople) and in the faith Christian faith, read these resources as a start.
Pope Boniface IV (608-615) (notice he's still busy kicking out temples of pagan worship in Rome, so Christianity was hardly in a position to reach the Arabs and that is why there is a tone of Christianity having "failed" in the Qur'an)
Pope Deusdedit (Adeodatus I) (political troubles, earthquake, leprosy outbreaks)
Pope Boniface V (619-25)
Pope Honorious I (625-38) (got comdemned as a heretic when trying to stop people from arguing about the true "nature" of Jesus Christ)
Of course after you read those Catholic Encyclopedia extracts you can search for more about the secular and political woes of those times and have an even greater understanding of God's perspective for the "timing" of the message of Islam.