One thing that's clear from the Qur'an is that Muhammad really didn't know an awful lot about Christian theology. He didn't know enough about it to adequately conform to it, nor did he know enough about it to be able to refute it. One example of the latter comes from the 5th chapter of the Qur'an, wherein Muhammad claims that on judgement day, Allah will ask Jesus if He told men to take Himself and Mary as two gods besides Allah. How is this wrong?
The first way in which it is wrong is that Jesus is not a god besides Allah. Rather, the Christian doctrine of the Trinity states that there is one God who exists in three separate persons. Jesus is neither a co-God, nor a second God, but is rather the sovereign Creator and ruler of the universe.
The second way in which this is wrong is that no Christian in all of history has ever considered Mary a god. There is one denomination which is notorious for its idolatrous worship of her, but even in Catholicism, Mary is not a god.
The extreme ignorance of Biblical theology in the Qur'an makes perfect sense if it was imagined by man or inspired by demons, but if it was truly Allah's word, we would expect a higher degree of accuracy. For this reason alone, we can reasonably reject Islam.