Why do people use hyperboles?

Best example I can think of in the use of hyperbole is from Jesus:

Luke 14:26-27: "If anyone comes to Me, and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be My disciple."

He is using this extreme language to say that compared to the love and joy the disciple would be entering into, whatever he'd felt for his family would be as hate....so different are the two forms of love and joy.

Hyperbole hear contrasts earthly and Godly feelings and experiences. That is it's main use, to point up what's obvious but overlooked or to show the truth or falsehood of a position or argument.