How private key is generated? I read here that: 


  If you could process one trillion private keys per second, it would
  take more than one million times the age of the universe to count them
  all. Even worse, just enumerating these keys would consume more than
  the total energy output of the sun for 32 years.


However this website http://directory.io says that they generated all private keys. Who is right? or what is it that I misunderstand ?

And why this (from here)


  A private key is a 256-bit value, meaning there are approximately
  1.1579e77 possible keys (There are about 1.2288e66 invalid values...
They never claimed to have generated all private keys, only the ability to generate any possible private key.

The web site dynamically calculates a set of keys for a given page number. It does not store every possible key.

The web site cannot be used to discover a private key for a particular address because there is no way to search for an address.