Religions are created by men. Christianity was created by God. You are right however on one point. It is calculated, according to Christ's death his birthday would actually be in October. Im not sure why we really celebrate it in december, but it doesnt really matter. If your birthday was on tuesday and someone forgot and presented you with birthday wish a week later would you tell them to send back the birthday wishes,gifts,hugs or whatever they do for you?
The fact of the matter is christ was born and then died so that we might have life and life more abundantly (john 10:10).
The day is irrelevant, December 25th is the day we christ followers HONOR and celebrate his birth.