I have 100 Pokemon and Professor Oak still doesn't give me the Eon Ticket. Why?

The Eon Ticket is not a Pokémon award. It is a Pokemon Event that has the Eon Ticket given to you. Sadly this event is over so there's no way to get it unless you know someone who got the real Eon Ticket into their game and if you do, you can mix records with them and it'll bring the Eon Ticket into your game. I believe the purple end of the Link Cable has to be inserted into the Ruby/Sapphire game in order for it to mix records so that it'll send its legit Eon Ticket over to Emerald but remember the Eon Ticket has to be legally acquired via the E-Reader if you have one in Ruby or Sapphire.