Bible Contradiction Du Jour: Genealogies of Jesus

In the spirit of the holidays I've been looking at biblical inconsistencies regarding the birth of Jesus. As a good example (excerpted from http://www.infidels.org/library/magazines/tsr/1993/2/2any93.html):

When, for example, I point out that Matthew's genealogy of Jesus differs substantially from Luke's, I am only stating an obvious conclusion that anyone can reach by reading both genealogies. Inerrantists will say, of course, that Matthew traced the genealogy of Jesus through Joseph, whereas Luke traced it through Mary, but there isn't a hint of any kind in the entire book of Luke that he intended his genealogy to be so understood. In the absence of evidence that this was what Luke intended, the inerrantist accomplishes nothing by merely saying, "Well, it could have been this way, so to have a case, you must prove that it couldn't possibly have been this way." No, a thousand times no! Such a position as this is not at all compatible with the nature of evidence. A lot of things could have been or could have happened, but just because something could have happened doesn't mean that it did happen. A copyist could have corrupted the text after Luke wrote it. Joseph could have been orphaned at an early age and then adopted by another family, and so Matthew traced the genealogy through the biological father and Luke through the adoptive father. Either one of these would serve as well to "explain" the inconsistencies as the traditional claim that Matthew traced the genealogy through Joseph whereas Luke traced it through Mary, but none of the explanations would work unless couldn't-possibly-mean-anything-else cases could be made for them.