Timing is everything

Jesus' birth was in the time of the governor Quirinius
- Luke 2:2,3-7

Jesus' birth was in the time of Herod
- Matt 2:1

The problem here? While Quirinius and Herod held different stations, the terms they served never coincided or overlapped.

Quirinius - became governor of Syria around 8 CE

Herod - died 4 BCE