“Seems it is Roman Catholicism that has the problem with accepting the inspiration of the Bible...”
No. Catholicism is fine. But yes, many Catholics do not abide by the Faith.
And many "Protestants" fail as well. Genuine Christians recognize the authority of the Divinely-revealed Scriptures and understand that what GOD says is a higher authority than what men say. That is why the Reformation stressed the priority of the sacred word over the traditions of men that, through the centuries, came to replace Scripture with traditions and rules proclaimed by fallible men as if they were as infallible as the Word of God.