Great question and one I have been interested in for a while. The fact is that the cult of Mithras and Christianity arose at nearly the same time which is to say the first century C.E. There was some scholarship which suggested parallels to early Christianity but for the most part they don’t pan out. Two of these are virgin birth and December 25th as the birth date. Neither of these are accurate. December 25th was already a feasting day in Rome for the feast of Saturn or the Saturnalia.
The Birth of Mithras from the Stone
Moreover Mithras was born from a stone as an adult. Mithras was a mystery cult, with blood rituals and completely male. It was a soldiers cult. On the contrary Christianity’s appeal in the early days was to women and slaves whereas Mithras appealed to high ranking army officers as well as common soldiers. It seems about the only things the two religions had in common were ritual meals.