Christians believe that Jesus is God who became man.
The usual Muslim approach is to point to a number of New Testament verses, which clearly show that Jesus is a man. Then to conclude: Therefore, he is not God.
However, obviously this argument misses the boat. Christians do believe that Jesus is a man. Therefore, the Muslim has not shown them anything new. The issue is the selective reading of the Bible by the Muslim. Obviously, the Christian understanding is the result of observing in their scriptures that Jesus is described with both human and divine attributes. Telling Christians about the human ones does in no way obliterate the divine attributes. The claims to deity by Jesus are the verses the Muslim needs to deal with, not those attesting to Jesus' humanity.
This example is the most prominent in this category, which is the reason that I chose it to give this fallacy a name.
However, it is the same fallacy when arguing about the Trinity. Christians do not believe that God is three in one. However, God is ONE. Every Christian will affirm this and defend this. If the Muslim shows Biblical verses that clearly state that God is one, then they have affirmed not contradicted the Christians. The evidence Muslims needs to deal with is those verses that show the divinity of Jesus and the Holy Spirit. The step from "God is one" to "therefore he is not three in one" is the logical fallacy.
After establishing that there is only one God, do we still have to ask what kind of God is it. A Unitarian or a Trinitarian God?