Matthew describes King Herod as the ruler during the time of the Nativity, and Herod died in 4BC.
According to Luke Jesus birth was at the time of the Census of Quirinius which was in 6 AD, 10 years after Herod had died.
Both statements cannot be true so there is an error in one of the gospels.
So my question is: if there is a factual error in one part of the bible does that make it totally untrue. No, i don't think it does. Surely accepting that there are these problems is preferable to trying to massage the texts into some sort of dishonest forced fit with each other? A bit of intellectual integrity would be better in the long run.
[With this specific example some people have tried to massgae the texts together by claiming that Quirinius was governer of Syria twice due to an inscription about an unamed person who was twice governor. This bit of wishful thinking has been largely discredited since the 19th century but still gets trotted out in defence of the inerrancy of scripture.
There is no mention anywhere of Quirinius serving two terms as governor, but we have evidence of two other people who served two terms of some sort of rule in the area so the inscription is more likely to be about one of them (Lucius Calpurnius Piso Caesoninus or Marcus Plautius Silvanus).]