Why do two negatives make a positive when you multiply?

Here's a rule everybody memorizes and almost nobody questions: two negatives make a positive. Negative times negative? Positive. But WHY? It sounds like a magic trick — turn left twice and somehow you're facing right. Let's pull back the curtain. It turns out this rule isn't a rule somebody invented to annoy you. It's the only way the math can possibly stay consistent.
First, let's agree on what a minus sign even DOES. Putting a minus in front of a number means "flip it to the other side of zero." Negative three is just three, flipped. So a minus sign is really an instruction: turn around. Face the opposite way. Hold onto that idea — it's the whole secret.
