The whole of the Western tradition of Christmas is not just a matter of one or two days of present-giving and family visits, there is a whole sequence of religious observances, services and so forth which the commercialisation of Christmas has succeeded in hiding.
As a celebration of some 2000 years of heritage – though, of course, it was not really celebrated until some time after the establishment of Christianity as a separate religion from Judaism – it has picked up a lot of nationalistic and cultural traditions, many of which have been adopted from other local religions and customs.
There is a fairly convincing argument that Christmas itself is based on the Roman festival of Saturnalia which itself was based on an earlier Babylonian festival. And that it was a Roman Emperor who decided to mix the events in order to make it easier for his subjects to call themselves Christians – a kind of spiritual hedging-of-bets.
External cultural influences and the date of the event, being midwinter in the northern hemisphere, has meant that many of the non-Christian midwinter traditions have been mixed in. The Father Christmas concept, Christmas trees in the house, putting objects into Christmas puddings these are all distinctly non-Christian.
However none of this should be taken as any form of criticism, or even a reason not to celebrate Christmas. The date and traditions are not important; the reason the celebration exists in the first place is.