We blieve that the biggest test the Christians had been put in was witnissing what looked like the crucification of Jesus. I believe that many (the majority?) of the Christians who witnessed it wanted to believe something else, they were basically in denial, they didn't want to believe that God abandoned his prophet, so when one of them came up with the story that he was the son of God and he did that to wash away the sins of the humans, they immidiately believed it because they wanted to believe that his death did not go in vein, they wanted mental peace.
Mohammad then later came and said that Jesus was not crucified, that god has protected him and has taken him to the heavens, so god did not abandon him.
The two big sects in Islam are the Sunnis and the Shiat, the Shiat basically have a faith similar to Christians of today, but not the same in terms of God/son relationship. When Ali (4th caliph and the cousin of the prophet) was killed, some Muslims felt so bad for what happened and they became the Shiat (or Shia'ah) of Ali, and they held him in a very high place from that time on (that is why the Shiat, one day in every year go out in the streets and start whipping themselves and shedding their own blood, it's the day that Ali was killed, like they are punishing themselves for it).
I personally believe that they have gone too far with their belief, and they started writing stories and teachings that they want to believe in, to make them feel better about what heppened to Ali. At least this is what I think they're doing (comforting themselves by saying that he was the chosen one and he was killed to protect us etc.).