Your friend is right, these famous "christian" holidays are actually remnants of paganism. Christmas was originally the winter solstice. It was adopted by Pope Leo in 800 AD under the urging of Emporer Charlemagne, the leader of the Celt tribes. Tribal Europeans were unconvinced by Christianity and battled the Romans for nearly 1,000 years to keep them out. Under the deal in which the Pope wanted to bring western Europe into its empire, they assimilated pagan traditions with the belief it would make the transition easier on the people. To this day Europeans keep the holiday as an ancestral tradition, yet many Christians in America are not aware of its origins (they lost most of their cultural knowledge in being assimiltaed to America). Its why the tree, Germanic people were practioners of animism, many of their myths contained the ideology of deities residing in trees or "oak nodes". Its why the acorn is still a holy symbol among Almanian people. I'm a german, and I admitt despite being a Kafir I have a special place for these traditions because I know my ancestors practiced this ritual for nearly 8,000 years.
Easter is pagan also, but on the eastern side, specifically it was the fertility holiday of the Goddess Astarte which was a patron deity of Rome. Hence the fertility symbols like rabbits, painting eggs, etc. Its a celebration of the changing of the seasons when the sun returns to earth and the greens shed again.
Most pagan religions have a cyclical view of time and hence celebrate the natural cycles of the seasons and astral bodies. Its rich in animism, ancestral worship and polytheism.
If Jesus did indeed exist, then he would have really been born around September, as the Bible records he came soon after the Feasts of Terbanacle. His birth certainly would have nothing to do with the symbology of horned stags (reindeers) old men (santa claus) holly (fertility plant) or the myriad of other things we associate with Christmas.