If your right hand causes you to sin

I was teaching the pre-teens on Bible genre. Explaining how the Bible is composed of various writing styles and how this has an effect on interpretation. An example that came up was the talion in the Torah compared with Jesus telling us to cut off our own hands in the gospels. In the former situation a legal text is meant to be understood by the nature of legal genre to be literal—the possibility of fines notwithstanding.

Your eye shall not pity. It shall be life for life, eye for eye, tooth for tooth, hand for hand, foot for foot. (Deuteronomy 19:21 ESV)

Jesus' words are thought by many to be hyperbolic.

And if your right hand causes you to sin, cut it off and throw it away. For it is better that you lose one of your members than that your whole body go into hell. (Matthew 5:30 ESV)

That it is hyperbolic can be noted by the fact that one does not sin because of his hand, we sin from our mind. And even if we did remove our right hand for stealing, what is to stop us stealing with our left?

The children understood all this, but what is particularly interesting is Jesus' contrast here. Why did he speak like this?

Jesus is teaching about the Mosaic Law. And the Law stipulates and limits punishments that were given for criminal offences. What Jesus does is turn the focus from what we demand occurs to others who have wronged us to what we must do to stop wronging others and God. Paraphrasing:

You know that if another (deliberately) maims someone's hand he is to have his hand maimed; well if you are sinning with your hand cut your own hand off. You remove a man's eye for causing blindness; remove your own eye when you sin with it.

Jesus is using what they do know about the Law to make them realise their own shortcomings. They know about cutting off the hands and plucking out the eyes of criminals, Jesus forces them to focus on how they were using their own hands and eyes.