First and foremost, I wish people would actually pay attention to the amount of people blocking traffic vs the amount of people taking part in demonstrations. The percentage is quite small.
Second, the media (primarily TV) controls general public opinion. This has been proved over and over by many focus groups (I can actually find them if people don't believe me). Since the pro-war camp, led by the President (just as every president does) are in the media every day, the pro-peace camp has to find a way to get into the media.
As much as I'd like to change it, TV reporters will only show up for good visuals and "clever" soundbites. Demonstrations provide both of these. I've organized more than one press conference, where we would be able to provide more substantial information, and have found TV media is much less likely to show up, if the press conference is not combined with sign holding, chants, etc.
So basically, we're forced into this situation of having to provide good visuals because TV media shows are concerend with ratings and not information. And unfortunately, the small percentage of long haired, tattoed, pierced people blocking traffic also provides better visuals than the large amounts of other people quietly participating in the demonstrations.
We're trying to change this by really focusing more on support for our troops coupled with a pro-peace message, and much more peaceful, lawful events. But there will always be a small group of radicals you just can't control, who make everyone look bad. And this is true on both sides.
Aside from what I mentioned before about the quantification of the settlement offer, the first reason that the story is biased is because the settlement has not been rejected, in spite of what the headline says.