It is not just a cave, but “this cave,” a certain cave. For Origen, as for the evangelists before him and for Justin, there is a verifiable particularity about the facts of Jesus’s conception, birth, and infancy. These events happened not “once upon a time,” but “in the days of Herod, king of Judea,” when “a decree went out from Caesar Augustus” (Luke 1:5; 2:1).
This pretty much answers why it has to be in a cave.
