write why do historians these day prefer to use the term BCE and CE are rather than BC and AD
Answers
Here are just a few problems with BC/AD:
They're inconsistent. BC is an abbreviation of the English phrase before Christ, while AD is an abbreviation of a Latin phrase anno Domini. It's very strange that going across the arbitrary division line between two years also requires a change in the language of abbreviation. Also, traditional convention says that BC comes after a date (e.g., 1200 BC, or year 1200 before Christ), while AD comes before the year in a date (e.g., AD 1200, or anno Domini 1200, which follows English style of in the year of Our Lord 1200). While that convention is no longer universally maintained, it's odd and confusing.
They're prone to misinterpretation. In particular, the language inconsistency noted above has given birth to a widely-held misconception that AD is an English abbreviation for after death (i.e., after the death of Christ). Obviously this is wrong, but it was actually the first explanation I heard as a child, which then caused great confusion when I encountered a teacher telling me that it meant something else in some obscure dead language. I'm not alone in having heard this false etymology, as many internet discussions will attest.
They're literally wrong. As noted in a previous answer, the birth of Jesus Christ is now estimated by most scholars to have occurred at least a few years earlier. (I've seen everything from 7 to 2 BCE -- and yes, in this particular sentence, using the abbreviation BC seems to me an oxymoron.) In any case, "common era" solves this problem by just admitting that we're using a common convention, which even Christian scholars now widely regard as inaccurate. But it's still a convenient and "common" way of referring to our "era" of year reckoning. Insisting that we hold onto the older style too seems to be promoting ignorance of the fact that the abbreviations are literally false.
They cause confusion. One item of confusion occurs because of the erroneous after death etymology above. (I distinctly recall asking someone about this when I was a small child: "So how do they number the years while Jesus was alive?" No answer.) But even if we understand what AD means, the convention can create confusion even when Christian scholars are trying to refer to, well, the years around the time of Jesus Christ. Because we know the birth year is off, any date in the first century BCE or CE is automatically a bit offset compared to the reference point that BC/AD uses. Dates in the early Church are a bit uncertain anyhow, but if a Christian scholar is trying to relate a possible date to the timeline of Jesus Christ's life, you have to do a little conversion in your head. Whenever I see BC/AD with a year within a few decades of Jesus's purported lifespan, I tend to think of an imaginary (sic) appended afterward. In other words, when a reference to the timing of Christ's birth should have maximum usefulness due to proximity of the dates, it actually breeds confusion.
Any one of these reasons alone wouldn't be enough to argue for a new convention. After all, there are all sorts of inconsistent and illogical stylistic elements in English usage. But when you take into account that the old meanings are widely believed (even by Christians) to be actually wrong, you now have a convention that's actively creating confusion.