Christmas is a memorization of the birth of Jesus Christ, the son of god. Integral to his designation is that his mother (virgin Mary) was not impregnated by a human, but by the holy spirit, hence can be described as "the mother of god", which provides unity to the holy trinity (through circular reasoning) and allows for his descend, crucifixion and resurrection.
There seems to be striking similarities between the story of Jesus and his mother Virgin Mary, and the Buddha's encounter with Mara, having the earth as his witness (bhumisparsha mudra) and the Buddhas lineage (which equally depend on circular view of death and rebirth).
It is unclear why Buddha's have their final birth on earth, but it seems to be a regularity in Buddhist cosmology:
The prophecy about Maitreya Buddha appearing in the human realm/earth (currently dwelling in Tusita heaven) makes the Bodhisattas of the Mahayana tradition sound similar to Christian theology, and sheds light about the connotations of the noble lineage (up to seven returns - one return - no return - arahantship) and the story of creation in Brahmanical/Abrahamic traditions (seven days of creation).Again, when the Tathāgata awakens to the unsurpassed perfect enlightenment, this earth shakes, shudders, and trembles. This is the fifth cause and condition for a powerful earthquake.
Thoughts.