Biblical genealogies are often cited as evidence for the reliability of the Bible. Some apologists claim that the genealogies in the Bible are supported by historical and archaeological evidence, yet the Bible includes a number of internal contradictions in these accounts which must call into question the reliability of these genealogies and of the Bible itself.
Genealogy of Jesus in Luke
One notable aspect is the Luke genealogy being much longer that in Matthew, giving the impression of the writers having very different ideas of how long ago King David lived from Jesus's alleged time. One apologetic has been to claim the Luke genealogy refers to Mary, not Joseph, with spurious claims that adoption could pass one into the bloodline of David. This is necessary because the genealogy in Luke derives Nathan, son of David, instead of Solomon (he alone was to carry on the bloodline, which had to be physical, thus necessiting it be Mary, not Joseph). However, women could not pass on the bloodline. Moreover, the genealogy clearly lists Joseph, not Mary. Apologists seek to get around this by claiming that when a genealogy ends with a woman, her husband is listed instead, despite no evidence of this practice existing. If Joseph was son-in-law of Heli in the Luke genealogy, it would have been clearly listed, as other parts of the Bible show in-law relationships, but there is nothing, and this does not change the lack of inheritance through mothers. They attempt to get around that problem by claiming Joseph adopted Jesus, with no mention of this in the Bible. Adopting Jesus would have meant acknowledging Joseph had not fathered him, and he was thus a bastard, for all anyone could know, thus negating any possible claims to anything, besides putting Mary in danger of being stoned to death for adultery.
Genealogy of Jesus in Matthew
The Matthew genealogy has its own problem. It lists the cursed king Jechoniah, none of whose heirs God decreed would inherit as punishment, thus negating that whole line of descent. The writer of Matthew seems to have been unfamiliar with this, although where he got this genealogy in the beginning is thus anyone's guess (is there a chance it was originally meant to disprove Jesus' claim, regardless of whether he existed?) Aside from all this, why Jesus needed to be descended from David through Solomon and be the Messiah is hard to grasp, as being God's son is far greater, except the obvious conclusion that originally he was not believed to be divine in any way (a blasphemous idea to Jews, we might note). There were many claimants to being the Messiah and so proving this was important.
Virgin birth and gods fathering children were distinctly pagan things likely added later to widen its appeal, since pagans were preached to. Prior to Jesus, there is no precedent in the Bible even remotely similar. The genealogies, perhaps even more strongly most anything else, prove the New Testament is composed of many competing writings. For, if Jesus is the son of God, why bother with it? 
Two different genealogies are given for Jesus, in the first chapters of Matthew and Luke:
|Matthew 1:1-16||Luke 3:23-38|
In tracing the ancestry of Jesus, Luke goes back farther than Matthew. Matthew describes the lineage from Abraham onwards and between Abraham and David both Gospels are in agreement with each other, and also with 1 Chronicles. Luke, however, goes back all the way to Adam, and there an anomaly is found:
|1 Chronicles 1:1-27||Luke 3:34-38|
- "Origen [...] argued that these were hermeneutic trip wires deliberately inserted by the holy spirit to make the reader think that bit harder about the New Testament’s other meanings – symbolic, ethical and allegorical – rather than the merely literal. "