I've been that student. Now I'm that teacher.
Here are dialogues that I've had:
Me: I honestly can't tell "if" it'll be useful to you. But I'd rather
we thought of it as "how" is this useful to you. How do you tell any
machine what to do? For example how do you tell the
washing machine to wash the clothes?
Student: (Most common answer) You push the button!
Me: Excellent! But part of school is to help you learn to think. So
instead of just showing you how to use the machine, I'd like you to
think about how does the button press make the machine wash its
clothes. How does the machine know what to do?
Student: (usually thinking) Ummm...
Me: Let's write down all what needs to be done when the button is pressed:
(we note some steps: start water, turn on the "rotating bucket", flow
detergent and stop after 45 minutes)
Me: Does the machine understand English?
Student: NO! It's a machine! (usually followed by giggles)
Me: Alright, so how do we "talk" to it? (carry this toward the notion
of a language that only computers can understand. Keep it high level
and dig deeper only if they're curious).
Me: Let's say that the machine only understands Python (or the language you're teaching). How can we tell the machine to do all the above steps?
This helps them at least understand why we need to program.
After this I give them an exercise on "giving instructions to someone". Intentionally ambiguous so that they can easily misinterpret it in hundred different ways. Like ask them to get me a Peanut butter and jelly sandwich the next day and we'll snack it in the class. Say it's for "me" (i.e., the teacher).
Intentionally critique them like "but I wanted it toasted" or with "less butter" etc., Students usually go "But you didn't tell us that! How do we know?". That's exactly what you want!
Now educate them to the benefits of being precise! When you give instructions to a computer you have to be very precise. With humans the more ambiguous you are the more confusing things get.
So, now we come full circle to why learn programming? It's the art of being specific - that is what we want to teach/learn. No matter what job you do, it'll come in handy. You'll realize what it means to be specific and "how specific" is good enough. The act of talking to a machine is just a fun way to teach you this. You may not use it, but at least you'll know something about it!
I've had great success with this with kids of all ages. It helps sink things in. Know why it's useful and what's the point are the best questions IMHO.