When I was a christian, I constantly heard about these 'contradictions' in the bible, and I either completely ignored the claims (as I imagine many still do) or I searched for some explanation as to why the contradiction was there.
After reading The Age of Reason by Thomas Paine, I saw these contradictions in a new light, that they were apparent, obvious and irreconcilable. One of the most acute contradictions are the conflicting genealogies of Jesus found in the New Testament.
The account in Matthew goes as follows (from christ back to David):
Christ, Joseph, Jacob, Matthan, Eleazer, Eliud, Achim, Sadoc, Azor, Eliakim, Abiud, Zorobabel, Salathiel, Jechonias, Josias, Amon, Manasses, Ezekias, Achaz, Joatham, Ozias, Joram, Josaphat, Asa, Abia, Roboam, Solomon, David. That is 28 generations in total.
The account in Luke is rather different, and is as follows:
Christ, Joseph, Heli, Matthat, Levi, Melchl, Janna, Joseph, Mattathias, Amos, Naum, Esli, Nagge, Maath, Mattathis, Semei, Joseph, Juda, Joanna, Rhesa, Zorobabel, Salathiel, Neri, Melchi, Addi, Cosam, Elmodam, Er, Jose, Eliezer, Jorim, Matthat, Levi, Simeon, Juda, Joseph, Jonan, Eliakim, Melea, Menan, Mattatha, Nathan, David.
Thomas Paine postulates that if Jesus' natural genealogy was 'invented' as it most certainly was (shown by the conflicting accounts), we then have no reason not to suppose that his divine genealogy was also invented, in simpleton terms, that he was not the son of god.
This kind of reason I found very intriguing because it uses the bible to prove christianity wrong.