Why are there nail growth differences  between humans and other mammals?
Cat claws are growing all the time, like horse hooves, or human nails. However, cats and horses usually use their claws/hooves, so they get shortened through mechanical action.

An indoor cat may need their claws trimmed if it doesn't use them enough (that's why cats will want to scratch everywhere), or if has supernumerary toes that don't normally touch the ground. Similarly, cattle that doesn't get to move will suffer from hoof overgrowth, which appears to be very uncomfortable to the animal.

Consequently, if you were to use your fingernails more often for digging and scratching, you wouldn't have to trim them all the time.