"When are we ever going to use this?"
Every math teacher's probably heard this at least once, and during some units, at least once a day. (There were years where I never heard it. How I long to go back to teaching that way. But I digress...)
Here's the answer I've taken to giving my students. It's three-part.
First, you may think right now that you won't use this specific math concept, or any math other than basic percent calculations with money. You may think you know what career you'll go into, and it's not one that involves math even a tiny bit. But when I was your age, I said the very last thing I would be was a teacher. When I passed my AP Calculus exam so my general math requirements for college were taken care of, I said, "Yes! I never have to take math again!"
Moral #1: It doesn't hurt to keep your options open. The more you learn—in all areas—the more doors you have available to you in the future.
Second, no, most of you will never have to do a geometric proof after finishing high school. You may never factor another quadratic equation after that, either, or sketch another box-and-whisker plot. But how often in life do you need to bench-press a hundred-pound barbell? Rarely if ever? So, why do so many people do weight training? To strengthen muscles so they will be able to use them in various other ways when needed.
Moral #2: Math builds up a part of your brain that might otherwise atrophy. Logical reasoning skills are always useful, and just like Chris Hemsworth's biceps, they don't magically appear from nowhere.
Third, why are you asking this in the first place? Are you really concerned with whether this is something you're going to use specifically in your everyday life? I'm pretty sure if you isolate specific tasks in most of your other classes, you'll find they don't mirror the activities of most adults. (I promise I haven't written a five-paragraph essay since high school.) I think you're really asking because I'm presenting you with something that isn't instantly easy for you. Your instinct, therefore, is to avoid something that requires effort unless you can see a direct need for doing it.
Moral #3: There is value in struggling. Many things are only worth the effort they require, making easy things pretty worthless. As for the direct need for doing it, see Moral #2.
This is a little ranty, but there's been a silver lining to these conversations lately. I rarely get through more than a sentence or two of one of my reasons before another student in the class pipes up with why they think it's important for them to learn the concept, even if it isn't obviously applicable to "real life."
Bless those long-sighted teenagers.
P.S. To be fair, I also have some students who ask the same question, but in a different way. They sincerely want to know the applications of a particular mathematical concept, because they like to see the bigger picture, to get an idea of how it's all connected. And that's always a question I'm happy to answer.