To understand Luke 14:26, you need to compare it to the very similar Matthew 10:37: “He who loves father or mother more than Me is not worthy of Me. And he who loves son or daughter more than Me is not worthy of Me.” Jesus is not teaching us to hate but he is using the word “hate” in a metaphorical sense to mean to love less.
Literary context also looks at the relationship between words and grammatical structure to gain any clues of meaning. This is a normal process that we do every time we read anything. From the newspaper to a novel, we practice these contextual principles.
All of this effort is to try to ascertain the original intent of the author. This is biblical study and interpretation. Once the original intent is understood, then the work of understanding in our times or the work of application begins. Otherwise, readers can attach any meaning they desire to a particular passage. No doubt it has been heard, “Well, this verse means this to me . . .” From that point, you can make the Bible say just about anything.
All Christian sects and cults use Scripture to defend their doctrine and practices. Their origins are by men and women who took a verse or verses out of context. They used a hermeneutical method that ripped the text(s) from the original intent of the author and applied their own.