To talk out of both sides of your mouth is to say something that contradicts what you said before. A person might give one opinion to one person and turn around and give the opposite opinion to another person. That’s talking out of both sides of the mouth, and sometimes preachers do it in their sermons. For example, if a preacher said at the beginning of his sermon, “Jesus is the Son of God,” and then a little later in his sermon added, “Jesus’ miracles are simply myths,” you’d...