Hey, I'm a BCE/CE Enjoyer, so I'll defend it.
You need some point in history to be year "0". There is no way you will get the whole world agreeing to one point of reference, not to mention how difficult it would be get everyone to start using that new point anyway. So we have to go with the birth of Jesus (or what people thought it was, we don't actually know when Jesus was born).
But the BC/AD terms just reinforce Christian social domination. We can't do anything about the actual year 0, but we can at least try and make the terminology neutral. And it makes evangelicals pissy, which is always fun.
Yes, because the gospels fundamentally contradict. One gospel mentions King Herod killing babies but he died in 4 BCE. Another gospel talks about a census as the reason Mary & Joseph were in Bethlehem, but the first Roman census in that region was in 6 CE (and it was for Judah, not Galilee where Bethlehem was but the author just likely screwed that up).