ROLE INHERIT

Hello,

I'm a bit new to Postgre, and I'm experimenting with the roles stuff.

I want to know why If I create a role called "administrator" (a group
basically, no login) :

CREATE ROLE administrator NOSUPERUSER INHERIT NOCREATEDB CREATEROLE;

And then create a user

CREATE ROLE admin LOGIN PASSWORD 'password' ON ROLE administrator;

admin doesn't have the CREATEROLE privilege himself, but because he is part
of a group that has it, why doesn't this fall back on him having it?

When I try to use that admin user to create another role, it says
insufficient privileges.

Am I missing something in this role stuff ?

Thanks

David