Why is the female voice (on average) one octave higher than the males?

Men's voices are generally deeper because the surge of testosterone released during puberty causes their vocal cords to elongate and thicken.

However, this is far less than one octave on average.

There are voice changes in gender all over the animal kingdom.

Women are smaller than men duh 

Mice and bats are high pitch and elephants are low and deep because of size