You cannot really understand how the world got to be the way it is without studying history. It makes no sense without it. If you care about understanding the modern world, you have to study some history. Want to know why some people are powerful, and some people are not? Want to know why some issues are framed the way they are? Want to know why some institutions work the way they do, and not another way?

History talks about these things. Sometimes it tells you a different story than those people, institutions, and issues will tell you themselves — which is why history can be threatening, powerful. There's a reason that autocratic rulers like to start by re-creating their own histories. Our stories about who we are, what we've done, and where we're going are always framed in historical terms. History matters to people, whether they acknowledge it or not.

If you want to prove to someone they actually do care about history, ask them their opinion on a controversial historical argument ("were the atomic bombings justified?") then assert the exact opposite position they took. They probably won't respond to it like it's a neutral or merely academic endeavor — they'll act like it's actually important to get it "right." Then ask them why they feel so strongly about it. It's not just a matter of being right vs. wrong, it's because these "controversial" stories actually are part of our national/political/individual makeup.

When taught correctly, history is the study of human behavior and the reactions and consequences of those behaviors. By studying and understanding the past actions and events we can hopefully be able to calculate probable consequences of future actions.