What's the meaning and motivation of Izaya's behavior in Episode 2: "Highly Unpredictable"? Durarara!! Episode 2 tells us about a girl named Kamichika. Near the end of the episode, after...


   ...Celty brings her to the roof to meet Izaya, he lets Kamichika to the roof edge. He tells her that a lot of people have jumped there, trying to persuade her that she's not a special case. After that he leaves, and Kimichika, after some hesitation, decides to jump. However, Celty saves her. 


Izaya's motivations here are a little confusing. Even if we forget that he has...


   ...ordered the kidnapping and rescue of a girl just for the fun of it,


he is being somewhat inconsistent by telling her about all the people who jumped from the roof. At first, it seems like he's helping Kimichika by showing her that her case is neither special nor too bad, and it is not worth jumping. It even seems to work at first, when the girl hesitates. However, when Izaya leaves, 


   she still decides to jump off the roof!


When Izaya sees Celty helping her, he doesn't act surprised at all, much as if he were expecting this scenario. However, he could neither be sure that


   Kimichika would jump nor that Celty would save her (I think he didn't even know that Celty hadn't left). 


So does this portray him as a person who knew that Celty would save her, and because of that the girl would once again understand that life's worth living? 

Because otherwise he's portrayed as a man who encourages another person to commit suicide just for the fun of observing it!
I think you're over-thinking this.

Izaya, for lack of a better word, is a troll. Period.


  One who posts a deliberately provocative message to a newsgroup or
  message board with the intention of causing maximum disruption and
  argument.
  (taken from Urban Dictionary)


But for real-life personal interaction instead of on the internet.

In fact, he is an amazing troll - as evidenced by his ability to read people's minds and predict their actions. Which in turn gives him a great ability to "toy" with people how ever he pleases.

For pretty much the entire show his actions are always to provoke responses in other people without regard to their well-being (or rather to intentionally hurt them in specific ways).




  he is being somewhat inconsistent when telling her about all the people who jumped from the roof. At first, it seems that his actions are directed toward helping Kimichika by showing her that her case is neither special nor too bad, and it is not worth to jump.


Since he admits to trying with people to see their responses, this type of inconsistency could very well be intentional to provoke a reaction from Kamichika.


  When Izaya sees Celty helping the girl, he doesn't act surprised at
  all, much as if he was expecting this scenario.


That's most likely because he knows Celty pretty well and it's common for her stick around and save people.


  Kimichika will jump nor that Celty will save her (I think he didn't
  even know that Celty didn't leave)


As a troll, it probably doesn't matter to him. But it's very possible that he knew Celty will save her and he wanted to see Kimichika's reaction after thinking she would die only to be saved.