When God dealt with the Jews in the Old Testament, He led Moses to write His Words in Hebrew for the Hebrew speaking people. Daniel, however, was under Babylonian captivity. His part of the Bible was originally written in the main language of his days, Aramaic. And the New Testament was written in the universal language of the ruling nation so that all who wanted to know God's Words could read them, Greek. God wants people to be able to read His Words, so why wouldn't He give inspired words in the main language to people now-a-days?
I guess the belief comes from the fact that most people don't believe that God can or will do what he says. The same God that rained the plagues on Egypt is still ruling today. He wanted men to have His Words back in the time of Moses and Paul, why would He change His mind about wanting us to have His Words today?
In this next clip, Dr. Sam Gipp covers this argument in a simple to understand way.