First course of priests began in Av or Nisan?
Once Ezra arrived at Jerusalem from Babylon in Av, the fifth month, he established the course of priests as a requirement of worship. He did it in accordance with the law of the LORD.
And he came to Jerusalem in the fifth month, which was in the seventh year of the king. For upon the first day of the first month began he to go up from Babylon, and on the first day of the fifth month came he to Jerusalem, according to the good hand of his God upon him. For Ezra had prepared his heart to seek the law of the LORD, and to do it, and to teach in Israel statutes and judgments. (Ezra 7: 8-10)
This verse indicates that the course of priest began in Av month (fifth month), instead of Nisan (first month). Rabbi Jose ben Halafta (150 AD) corroborated Ezra.
Whence do we know that the second Temple was also destroyed on the 9th of Abh? We have learned in a Boraitha: “A happy event is credited to the day on which another happy event happened, while a calamity is ascribed to the day when another calamity occurred; and it was said that when the first Temple was destroyed it was on the eve preceding the 9th of Abh, which was also the night at the close of the Sabbath and also the close of the Sabbatical year. The watch at the time was that of Jehoyoreb, and the Levites were chanting in their proper places, at that moment reciting the passage [Psalms, xciv. 23]: “And he will bring back upon them their own injustice, and in their own wickedness will he destroy them”; and they did not have time to end the passage, which concludes, “yea, he will destroy them–the Lord our God,” before the enemy entered and took possession of the Temple. This happened also at the destruction of the second Temple. (Jerusalem Talmud, Tractate Taanite, Chapter 4)
Any calculation of Jesus birth leading to September or October was based on false assumption that the course of priests began in Nisan. In fact, Ezra 7: 8-10 and historical testimony pointed to Av as a month the course began in. Hence, Bible indicates that Christmas falls on December 25.
1http://www.jewishvirtuallibrary.org/jsource/Talmud/taanit4.html; access 26/4/2015