I think he's just crazy and just likes to mess with him.

Just think that Izaya-kun likes messing with Shizuo because of the reaction he always gives him he does mess with him and I find that he enjoys that and it doesn't stem from hatred.

yeah I think they just like messing with each other too

Maybe no! He just loves to troll!

This is just my take on it, but to me it seems Izaya is envious of Shizuo because he is surrounded by friends, in difficult moments Shizuo has his brother beside him, has Shinra, has Celty, Tom and a lot of people that really love him, and It seems that even if Izaya tries to love all humanity, no one requites him. Also In the last episode when Izaya got punched by Simon, Simon said "Don’t try to fool me, you just don’t want to lose to Shizuo, right? You have some kind of complex with him." so I think he just has mixed emotions on Shizuo, like jealousy, envy, admiration, etcetera. Aswell as i agree that he just likes messing with him more than most, because he once said "Shizuo is 'unpredictable.' but really Shizuo is one of the most predictable people ever, anyone with a basic understanding of human psychology can pretty much predict how Shizuo will react in most situations, and considering how Izaya prides himself on far more than a basic understanding of humans and how they work, all I can figure is that Shizuo's "unpredictable" actions fall more along the lines of "behaviors Izaya really doesn't like", it's not that they're unexpected, but that every time, Izaya deludes himself into believing/hoping Shizuo will respond in a way that's amenable to him and his manipulations.

Yes, but not nearly as much as Shizuo hates Izaya.

rikku_chan: THIS^^

rikku_chan has persuaded me with her words of wisdom XD

I have... link...

i think izaya hates shizuo because he can't control him and he can't be swayed by reason

I don't think it's quite hate

Izaya does hate Shizuo, supposedly for his unpredictability. However, I think there's more to it. In the anime, Simon theorizes that Izaya simply doesn't want to lose to Shizuo, which may indeed be the case. It's also possible that Izaya is jealous of Shizuo's many friends, while he himself only has Shinra. I think, however, that he mostly just doesn't like Shizuo because Shizuo just randomly decided to hate him. For those who have read the novels (and least up to volume nine), Izaya changed a lot after the incident with Shinra and Nakura in middle school, which severely affected him. Up until then, he'd just been a bit odd, and, assuming he met Shizuo in his first year of high school, it probably hurt him that someone so instantly hated him, especially since Shinra knows what he's like and doesn't mind at all. I think that was the first time Izaya really felt lonely, because, as Shinra notes, Izaya is more fragile than he lets on. Ah, but that's just me.