Reasonable people would think that *neither* side has cause for violence, because violence only perpetuates violence.
Reading the CNN story again, I don't see them "actively and loudly" supporting Israel. The current story basically says:
1) Israel attacked the Beirut airport in a "sharp escalation" of its military campaign
2) Hizbollah fired rockets into Israel
There are quotes from both sides, and if anything Israel is being painted as much more aggressive. The Lebanese Interior Minister is quoted as saying the Israeli attack is a "general act of war", Abbas is quoted as saying that the attacks won't bring peace, Bush is quoted as telling the Israelis not to get too aggressive, and the Israelis are quoted basically trash talking about how severe and harsh the response is going to be.
Casualties on both sides are given, and are reported as being worse in Lebanon.
I don't see anything supporting one side or the other, so the only thing I can see that you might be complaining about is that CNN isn't directly supporting Hizbollah's position. I don't see that as biased at all.
Personally, I think both sides are off their rockers. And I read a lot more than just CNN and al-Jazeera.