I found an official statement by the Society on the matter and it states a number of the reasons mentioned in some of the prior posts - and it refutes the accusation of it being for anti-Christ reasons. See https://wol.jw.org/en/wol/d/r1/lp-e/102009094 which says the following regarding it:
"Awake!—2009
g 3/09 p. 30From Our Readers
Ancient Manuscripts—How Are They Dated? (February 2008) This article upset me. It is my understanding that C.E. stands for “Common Era” and B.C.E. stands for “Before the Common Era.” In all of my 70 years, I have seen the terms B.C. and A.D. used as a time reference, referring to before and after the birth of Jesus. It seems to me that using B.C.E. or C.E. somehow denies the birth of Jesus.
R. W., United States
“Awake!” responds: Although A.D. (Anno Domini, meaning “in the year of our Lord”) and B.C. (before Christ) are used in lands where professed Christianity predominates, we have chosen to use the terms C.E. (Common Era) and B.C.E. (Before the Common Era). Why? First, there is considerable evidence pointing to the year 2 B.C.E. as the date of Jesus’ birth. Second, the literature printed by Jehovah’s Witnesses is widely distributed in languages read by many non-Christians. Third, the title “Christ” means “Anointed One.” Jesus became the Messiah, or Christ, when he was anointed with God’s spirit at the time he was baptized in 29 C.E. (Matthew 3:13-17) Thus, Jesus was not born Christ; he became Christ the year of his baptism. Significantly, the descriptions C.E. and B.C.E. are growing in usage, and they appear in almost all modern dictionaries and in many scholarly works. Please be assured that Jehovah’s Witnesses consider Jesus and his sacrifice indispensable to the outworking of God’s purposes and our personal salvation."
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Update: I now notice that Jeffro posted the information from the Society before me, however my post gives the web page where the Society makes its statement.