Because that was the dominant language of commerce and education all around the Mediterranean at the time, and had been since the days of Alexander the Great (who was "just slightly" BC). A great many Jews outside the bounds of Judea spoke, wrote, and read Greek and spoke no Hebrew. But the point isn't the language, it is the books comprising the Testament.
"But then claiming a BC Greek OT, you can only go back to 400 for your NT ?? That is because the Catholic NT came from Alexandria after 325 AD. It had been sitting being mutilated and corrupted by Origin and his ilk in N. Africa until Constantine ordered 50 copies of it, which ended up in Rome. Original? Not by a long shot. Byzantine/Antiochan NT copies were all over Asia Minor, along with a Latin OT (160 AD) long before that.
Oh, good grief. Are you REALLY that obtuse??? Of course there were earlier versions of the NT, but no general agreement as to exactly WHICH books should be included, and which left out. General agreement on that topic finalized around 400AD.
There are many reading these who will now begin to get the picture that all the story isn't told by Catholic historians. Many of the pieces of the church history puzzle are help by historians outside of the Vatican's approved list of historians. And the truth about manuscript evidence is not all in the hands of Catholic scholars either.
Whenever an organization that is trying to protect and defend its own position as THE Church, and as definitive Christianity, and has a history of having murdered people by the hundreds of thousands over just that (their own authority), then all history written and taught by that organization must be challenged and questioned.
Churches and Christians who are NOT trying to tell the world that their own visible church and system is infallible or supra-authorative are more likely to be honest and open and spread their research out further to seek truth about history.