Question #1 from the OP
Christianity’s central concept (from my understanding, please add on): Christ’s incarnation and sacrifice on the cross in order to atone for our sins that we could not atone for by ourselves
This question should be asked from the christians because the Muslims do not believe in incarnation. They do not believe that any one can take away the sins of others by dying on the cross. The Muslims do not believe that an innocent person, beloved of God (Jesus) may be punished for sins of others. The Muslims believe that God can easily forgive the sins of all people without any one’s blood provided that One repents and seeks forgiveness.
Also Jesus ha ddone enough good things for the salvation of the Jews by his teachings and lectures and guidance. That was much more than going on the cross.
That is the Islamic teaching about the Question No. 1.
Question #2 from the OP
Islam’s central concept: ?
Islam’s central concept is to obey Allah only and believe in Him alone as the God. Also to believe that Muhammad is the messenger of Allah. So nobody can go to Allah except through Muhammad.
In the time of Jesus, nobody could go to God except through Jesus.
If Muslims trace their history back to Abraham, why weren’t they Jewish, and thus Christians now?
This question could be replied in many ways. We Muslims can easily question the creation of christianity. Jesus did not want to start a new religion. He only came for the Jews and wanted to reform the Jews, to cure their bad habits and mistakes, keeping to same law of Moses.
Those who followed him were all Jews for a long time. They were not christians.
So please tell us from when they became christians?? And what was the need to do that?? Did Jesus tell them to break away from the Jewish race and start a new religion?? I hope not.
So if it was alright for some people (who were Jews) to start a new religion called christianity (and we admit that faith because it has come to stay), it was similarly alright for the Muslims to remain on their new faith.
Jews had the guidance from God.It was finally handed down through Moses, until Jesus was the last prophet amongst the Jewish line. When Jews were spoiled, there came Jesus. God sent him. It was not right for Jesus to follow the mistaken people i.e. Jews. It was the duty of the Jews to follow Jesus.
When they did not follow Jesus, a new religion emerged.
Similarly, When the christians forgot the teachings of Jesus, as we Muslims believe, Allah sent a new messenger with guidance. He preached in Arabia and invited all the world to follow him. It was not the duty of Muhammad or Muslims to merge into misguided christians. It was the duty of mistaken people to follow Muhammad. And there were many pagans in Arabia nd India. They needed immediate guidance to take them away from paganism. Church could not do that.
That is how it was not necessary for Muslims to become christians. The Christians had not become Jews. I hope you understand. The Teachings of Moses were the best and should have been followed. They should be followed by the Jews even now.
Similarly, Islam teaches that christians should follow Jesus in a good faithful way even now. There is no harm. But the salvation is now resting with the teachings of Muhammad, that is the last message of God to mankind.
Also there is no binding, no force, no compulsion on any one to follow Judaism or christianity or Hinduism or Islam. Every one will have to answer before God on the last day.
If the last question (#3) is a sort of good wishes, the way the things should have been, should have gone, then I admire the good wishes of the OP.