Indeed Prophet Muhammad PBUH or his Sihaba Ikram Ridwanullah Majmaeen or Tabaeen, or TabaTabaeen never celeberated Eid Miladun Nabi (Birthday of Prophet) but by Fatimid Caliphate nearly 900 AD. Means after 3 centuries of the times of Prophet Muhammad PBUH.
We are following this Hadith (Sahih al-Bukhari 7320, Book 96, Hadith 50)
"The Prophet PBUH said, "You will follow the ways of those nations who were before you, span by span and cubit by cubit (i.e., inch by inch) so much so that even if they entered a hole of a mastigure, you would follow them." We said, "O Allah's Messenger PBUH! (Do you mean) the Jews and the Christians?" He said, "Whom else?""
If someone does agree with me then he or she should take a pictures on Eid Miladun Nabi and Christmas and then mix them and its not easy to differentiate them.