why do people go from christian to muslim or vice versa?

Here are some chapters from the Quran in the source that are not hard to understand, listen to the interpretation while reading the English interpretation its much easier that way.

Islam teaches that the Bible is in fact a revelation from God but was altered and changed from the times of Jesus who in Islam is like Moses to Christianity, an honest prophet of God. And the Quran in the last revelation from God and the only one that is being preserved by God and Mohammed is the final prophet.

Islam is strictly monotheist meaning non to be associated in worship besides God. Muslims believe that Jesus never intended himself to be worshiped or prayed to rather he had the same basic message of all prior prophets.

If Catholics are Christians, who believe Jesus is God as well as Son of God, who died for their sins and resurrected, than ascended to the heavens;

And if Protestants are Christians who believe that Jesus is Son of God who died for their sins;and resurrected, than ascended to the heavens;

Than the Muslims are nothing different but Christians who believe that Jesus was the Prophet of God and he never died for nobody's sins and was never resurrected, but ascended to the heavens alive.

If one is willing to blindly believe that God died for his/her sins than they remain a Christian.

But for a born Christian to believe God died for their sins is 'non sense' than they simply make the switch.

In a nutshell, a Muslim is non other than a Christian who cannot accept that God died for his/her sins and that Jesus was merely Gods prophet.

Islam and Christianity teach fundamentally different things. Religions are differentiated primarily by theology and philosophy, not ethics. While both teach similar ethical standards, they have radically different views of God, mankind, the life, the afterlife, and basically every other point of theology, with the most important being Christology.

I'd say they decided thier current religion failed them in such a major way they decided it must be wrong. Yet the comfort of living a dogmatic life. Along with the idea of being accountable for thier own thoughts. Forced them to choose a new faith. Besides they can have the comfort of still being allowed to hate the jews.

They are swayed to the other side by crafty apologetics.

No, Islam and Christianity do not teach the same thing. They are fundamentally different in their theologies: E.g. trinity vs unitarianism, human atonement, Jesus as God or as merely a prophet et cetera

you're poorly informed to ask this question.

if you never read th quran then you may reckon this:

http://quran.com/