Stop thinking about programming as the end goal. Start to think of it more like a means to an end the same as spoken language, mathematics, shopping and things like that. This way you are encouraging your child to do what they want and ensuring that they have the tools with which to do them. Programming is just a tool, the more people are able to program the less of a barrier it will be to cool business ideas. You wouldn't say "should I encourage my child to learn to speak?" You'd say it was incredibly important to every day living.
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