Two Sides of the Coin?

I occasionally debate with a fellow online about Religion (me being an Atheist (I don’t know there is no god/are no gods, but I don’t see enough evidence to believe in any) and him a Christian). After the last debate, he challenged me to research the “Historicity of the Resurrection of Jesus”. I’m doing that now–it is a subject with a lot to say! But in this research I was side-tracked by the issue of the Genealogy of Jesus Christ.

How does the Genealogy of Jesus work? Why is this an issue? Well, there are two places in the New Testament where it is listed–Matthew 1:1-17, and Luke 3:23-38, and they are totally different. The big question is: Why are they different?