Why is Earth's biodiversity greatest near the equator?

Because the climate is better suited to sustain life. In the tropics you don't get high fluctuations of temperature. I used to live in Indonesia, it's pretty much a high of 30-33 degrees celsius all year round. Now I live in LA, temperature varies from 10-40 degrees celsius over here. Go further north and the temperature variance is greater. Life has to adapt to freezing cold climate as they move away from the equator, only a few can do that.