Why we can't use the diode instead of a battery to turn on a light?

Because a diode doesn't have any power, that's where the battery comes in..

I am not big on electronic knowledge, but a diode is basically a one-way valve. It has no electrical storage properties.

What makes you think a diode can be used as a power source?

Generally speaking diodes are used to rectify (convert) an AC source to a DC source. This is accomplished by a"Diode Bridge"

Diodes only allow current flow in one direction. The next step in the process would be to smooth out the pulsating DC to as flat a signal as you can get.