At first the thing that captures you is a huge world to explore, levels to gain, secrets to unfold etc etc. It's pretty big, you want to see more.
After that you become eager to get to the level cap, because you've been having fun all the time and people say the game doesn't get REAL fun until the cap.
Once you reach the level cap there are stats/specs/professions and gear to improve, which will keep you occupied for ages, farming items, money, bosses etc.
Apart from raiding/pvp, the endgame consists of daily quests, which can be done once a day. Some actions can also be performed once a day. These quests and actions reward or have the possibility to reward you with valuable items such as materials to craft better gear, emblems to buy better gear or simply exclusive mounts and vanity pets.
Then there's heroic dungeons. They reward gear or emblems to purchase gear, you're limited in how often you can do these each day.
So for optimal results, you're going to be playing every single day, for several hours in order to farm everything you're needing/wanting to have.
In the end, the addiction just creeps in like that. You want to have the best/rarest stuff available as fast as possible, and with such goals in mind, you don't really realize how repetitive your gaming experience has really become.
You're not experiencing it as "doing the most annoying dungeon over and over" or "Doing the same 25 quests that require to kill the same 20 mobs over and over", you're just working hard on getting what you want, and skipping it all for a day would only delay you obtaining desired items by another day.