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Scholars have used the C.E./B.C.E. convention for years mostly because it replaces a religious-leaning convention with one that doesn't show bias toward one religion. The idea is, in part at least, that using B.C. and A.D. suggests that Christianity is the benchmark by which all else is measured. At the end of the day, this is another one of those things that one can make a case for both arguments. Indeed, Daniel Wallace, writing on the bible.org website (here) presents a cogent case from an evangelical Christian point of view for C.E. over A.D.
In the church, we will continue to use the traditional abbreviations because they express what is true for us: Jesus is the axial moment in our history. But it really shouldn't be a matter worth getting all bothered about otherwise. Using the newer abbreviations acknowledges the fact that we do live in a pluralistic society. It also replaces an obscure Latin abbreviation, Anno Domini, with an English one. But, truth be told, the BBC's critics are right when they note that changing the terms doesn't change the fact that we still count our years based on the birth of Christ—in our calendar, at least. Now, in Thailand, the year is 2554 B.E. (Buddhist Era), and Christians in Thailand count the years from the Buddha just as readily as do Buddhists. On a daily basis no one stops to think why it is 2554 instead of 2011. Just like here, in Europe, and even in Britain, we use 2011 day in and day out and rarely stop and say, "Oh, yes, it is 2,011 years since Christ."
Maybe some people take this abbreviation stuff too seriously. Ya think.