The belief that the Bible makes this exception is a very dangerous one. It is based on a misinterpretation of Matthew 5:32 which says: " That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery."
The modern translations use the word 'adultery' rather than 'fornication'. The word for adultery comes from the word 'porneia' which refers to fornication.
Pastor John Piper explains: