They don’t have lights, but they reflect light from the sun at certain times of day. Another way to think about it: these satellite can be experiencing broad daylight hours after the sun has set at the surface. Similarly, when you’re seeing the Moon at night what you’re actually seeing is daytime on the Moon and it’s often enough to light up the landscape around you because you’re looking at an object that is experiencing daytime while you aren’t.

The question then becomes: can’t the satellite be made darker? And the answer is they are already pretty dark. The moon, for example, has an Albedo (measure of reflectiveness) of 0.15, which is similar to asphalt and it can still dominate a night sky. SpaceX satellites have an Albedo of about 0.11, so astronomers are essentially having to deal with thousands of tiny and unpredictable Moons drifting across the sky. I can’t find the article now, but I recall reading that the albedo would need to get down to 0.002 to become negligible; I just don’t see that happening.