The apologetic rebuttal to Gospel contradictions is that is actually adds to the credibility of the stories, in that it shows that they didn't conspire together to lie. Honest testimonies from different perspectives will often contradict due to imperfections in observations and memory. While I agree with the argument in principle, the question simply becomes to determine what level of contradiction is present – a low level supports the stories' honesty, a high level discredits the stories' accuracy. For this reason, I will be disregarding the minor contradictions and focusing on the big ones.
One point that is import is that Mark 16:9-20 is not part of the original. Conservative theologians agree with this, otherwise I would feel the need to defend this claim.
The Empty Tomb:
In Mark, the women come to the tomb where a young man tells them Jesus is risen. They tell no one (Mark 16:8) – this detail clashes badly with all three other Gospel accounts. How did the disciples hear about the Resurrection? The testimony of the women is only relevant if we know what their story was.
(I have since backed away from this argument.)
In Matthew, the women come to the tomb and speak to an angel on the stone (28:5). Here, the women follow instructions and tell the disciples (28:11).
In Luke, the women report to the disciples (24:9 - note Peter in particular) that they have seen the Resurrected Jesus. This again clashes with Mark 16:8, but it gets far worse when we look at John.
In John, a highly upset Mary Magdalene tells Peter and John that Jesus' body has been stolen. This is not to be confused with Luke 24:9 when all the disciples were present and the news was incredibly good rather than upsetting. Peter and John find Jesus' tomb on their own (20:8). The Mary tells the rest of the disciples. Surely this time much line up with Luke 24:9. But in Luke, they don't believe her, so Peter leaves to check it out for himself (Luke 24:12). In John, Peter has already been to the tomb, because he saw the tomb before Mary sees Jesus (John 20:11). Therefore, either Luke 24:10-12 is fictional, or the classic Sunday School story of “they have taken away my Lord” never happened.
Location of Appearances:
In Matthew, both the angel (28:7) and Jesus (28:10) tell them to tell the disciple specifically to go to Galilee, just as in Mark 16:7. In Luke, the angels remind them that while Jesus was in Galilee, he told them he would be Resurrected (24:6-7). Now, if you're not paying close attention, you just missed like I missed it the first hundred times I heard the story. In Matthew and Mark, the young man/angel/Jesus tell the disciple to go to Galilee, while in Luke, Jesus told them something while he was in Galilee.
Remembering what was said exactly is not that big of a deal. (It's a good rebuttal to the reasons to believe the story as a decent part of the testimony is what was said, but it's not a reason to disbelieve.) The big deal is that Matthew, Luke, and John's Resurrection appearances need these words to be as they appear in each book. In Matthew, Jesus is seen in Galilee, which is fifty miles away from Jerusalem, while in Luke, Jesus is seen in and around Jerusalem.
So did Jesus tell the Marys to tell the disciples to go the Galilee? Notice how wrong one story must be. Matthew repeats the instructions twice and Mark once – if they're wrong, then the accounts of the “young man”, the sighting of an angel, and the sighting of Jesus contain only words that were not actually spoken. If Luke is wrong, then he changed the words of the risen Jesus to make his story flow.
The Story Grows:
The order of writing was Mark, Matthew, Luke, then John. In Mark, there are no Resurrection or angelic appearances, save for the passage which is known to have been added. In Matthew, there is one, in Luke there is three, and in John there are three with far more details.
The Role of Women:
Also, as time goes on, the role of women is demoted. Now, as apologist tell us, women's testimony was not considered to be reliable at this time. The reason apologists tell us this is that the best reason for the Gospel writers to have for including women if it was true. I agree to a point – the Gospel writers didn't make up the stories, but rather used stories that they were circulating. But the testimony of the women is the part of the Resurrection accounts that differ the most sharply, so it's hardly the place to look for strength.
Also, consider the evolution of the stories with time: In Mark, women's testimony is 100% of the evidence. In Matthew, this is thinned out a bit as men see Jesus as well. In Luke, Peter makes it to the tomb himself at the prodding of Mary. In John, Peter and John make it to the tomb before Mary finds out herself. Seen in the light of “women are talebearers,” the story is growing and shows evidence of changing.
Is it not odd that Mark only records Mary talking to a “young man?” A harmonization would require Mary to have spoken to both angels and Jesus himself, yet Mark only bothers to record her conversation with an angel while somehow failing to mention that it was an angel. This falls short of a contradiction, but also short of believable narratives.
The contortions an apologist must go through to defend the Gospels' reliability are greater than what must be supposed to conclude that many or all of the alleged sightings of Jesus didn't ever occur, and the remainder were whatever it is that all other religions and cults are based on. Once one fully understands why they don't take seriously the miracle stories of any other religion, they will understand my hesitancy to believe the Bible's contradictory accounts of the extraordinary.
It is easier for me to make sense of how an explosive religion could start without the Resurrection than it was for me as a cessationist to make sense of sincere Pentecostals. There are options other than someone is tell the truth, telling a lie, or is insane. Sometimes people are just wrong.
If I place the ideas that the testimonies are/aren't reliable on a 50/50 level, the contradictions point to unreliability. This does not even employ an anti-supernatural bias and overlooks the fact that Christianity has the burden of proof, or at the very least, the burden of evidence.
Even the Biblical accounts give poor evidence for the Resurrection. If Christianity has a strong point, this should have been it. In my case, it was these arguments in particular that broke the camel's back. I became an evidentialist three years ago because I saw the flaws of presuppositionalism. But now I saw that many are presuppositionalists because they see the flaws in an evidential approach.
Now I was neither one.