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Whilst Christians and Muslims believe many things in common, there is a profound difference in belief when it comes to Prophet Jesus (peace be upon him).
We need to go way back to find an answer to our differences. Both Christians and Muslims believe that the first human beings, Adam and Eve, sinned against God and were punished for their offence.
In the Christian version of the story, Adam and Eve are expelled from Paradise as part of their punishment, woman is made to suffer in childbirth as part of the punishment and their descendants forever carry the guilt of their sin.
Many, many centuries later, the authors of the gospels chosen (from among many) by the early Church, led by the writings of Paul, urged people to see that this sin could only be forgiven by a sacrifice to God from a special Savior, who would save the people from their sins.
The sacrifice could only, in fact, be the death of one equal to God, otherwise humans would not be giving God anything He did not make.
Much writing, and many more centuries of Christian debate later, the opinion that Jesus was equal to God and that he died on the Cross became the prevalent view, although many famous Christians have held the view that this was not the case.
For Muslims, the matter is much, much simpler. God can do whatever He wills. He only needs say to a thing “Be” and it is. For Muslims, Adam and Eve did indeed sin, but they repented and were forgiven, since God can easily forgive, is the Most forgiving, and loves to forgive those who repent.
There is no collective guilt and no collective punishment of the innocent along with the guilty. God is the Most Just and would not put the burden of the guilty onto the innocent. So, there is no need for a Savior.
The fundamental difference here is that for Christians, their faith leads them to need an intermediary who will mediate between God and men. For Muslims, there is no need for popes or priests to act on their behalf. They will each answer to God on Judgement Day for how they have lived their lives.
And each person has the opportunity to have a relationship with God, seeking nearness to, and forgiveness and mercy from Him in this life without help from a hierarchy of religious clergy or from a savior.
Finally, as for this or that quotation from Scripture proving one thing or another, we need to remember that the existing Christian scriptures are a very selective collection from many other scriptures which were rejected.
Their authorship is unclear and there exist no original copies anywhere. Therefore, the authenticity is suspect.
I hope this helps answer your question. Please keep in touch.
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UK Pastor to AboutIslam: ‘Muslims & Christians Worship Same God’