What classes should I take in highschool to major in engineering?

Math and Physics, and also Chemistry if you can. If your school has a class in programming and you have time in your schedule, you should take that too. Even regular engineers have to endure some programming.

You should take all three to the highest level possible. Two reasons:
1. these subjects are difficult, and the more you can learn in a high school environment, where learning is easier, the better.
2. Engineering schedules are jam packed. If you get the chance to take advanced placement (AP) tests for these subjects, take them and knock these credits out in high school so you can spend your time in college on more interesting and specialized stuff.

If you don't knock out any AP science classes in high school, that is perfectly okay. Most engineers do not. But if you want to make your life significantly easier:

Calculus AB is worth 1 semester of math (Calc I in collge) Calculus BC is worth 2 semesters (Calc I and Calc II) That's an entire year's worth of math courses if you have the opportunity at your school to take Calc BC, or half a year with AB

AP Physics comes in two variets, AP Physics "B" and AP Physics "C". AP Physics C is a more difficult class, as it includes the calculus components to physics (taking this and an AP Calc class in the same year is the best way to go about it). Not all schools will accept the "B" version for physics credit, and when they do you usually need a "5" (highest possible score) to get the credit. AP Physics comes in two sections, Mechanics and Electricity and Magnetism. It's one class in the school year, but two exams. You can take both if you wish. Each exam is worth a semester of physics, so if you knocked out both, you could also get credit for a year of physics classes (and labs) before you set foot on campus.

AP Chemistry can knock out a semester of chem, and many engineering schools will let you get out of the freshmen year programming class if you prove to them (No AP exam for this, you gotta take their test) that you already know programming.

But even if you don't take or pass any of those above exams, the classes in college will cover very similar material, so you'll have a huge advantage when you get into college. If you can ace all your classes freshmen year, your GPA senior year will be very grateful!