If the speed of light is constant, why does time slow down at high speeds?

Because everyone measures light at the same speed c, the universe has to adjust time to make that possible. Imagine a “light clock” that ticks when a photon bounces between two mirrors. For someone at rest, the photon travels straight up and down. For someone watching the clock move fast sideways, the photon follows a longer diagonal path, but its speed must still be c. A longer distance at the same speed means each tick takes more time, so the moving clock ticks slower. That’s time dilation: to keep light’s speed constant for all observers, time slows down for objects moving very fast.