That's because it was that fool's fault for bringing a human to their borders in the first place. That man is an idiot for bringing misfortunes of his own people. Typical.
Actually they didn't.
What happened was an elf who was part of the Emerald Knights fell in love with a human. The other Emerald Knights grew suspicious of their comrade becoming distant, so one of them decided to follow him one night when he went to the human settlement of Red Crossing.
Unfortunately they got there too early, so the woman ran forward (believing the figure in shadow to be her lover) only to be struck down by the other Knight's arrows, thinking she was seeking to attack them. That is when the elf who was her paramour arrived and refused to leave her body. So when the mob arrived and found an elf over a death human, they killed him, thinking he was her murderer.
The other Knight hoofed it back, but the news of the paramour Knight's death had already found its way back, so that the truth of what really happened was eventually lost in the retelling and as more mobs began to form seeking a reprisal.
Similar to The Masked Empire, the death of a peaceful and tolerant elf who believed in coexistence, ended up becoming the martyr and rallying cry for those seeking violence and hatred against humans. Which leads to the irony being that if they had lived, those same mobs would have probably killed them for "siding with the enemy".
While the Elves did unwitting fire the first shots in the conflict, it was a misunderstanding and the racial tensions between the two groups made it a powder-keg that would have likely gone off at some point regardless.
As we learn in JoH, it's entirely possible if Inquisitor Ameridan had still been around to convince the Elves to lend aid during the Second Blight, the entire Fall of the Dales could have been averted. Rather than Orlais resenting the Dalish for not helping their own fight against the Darkspawn, both could have united against a common foe and built up stronger ties of co-operation and trust between their disparate peoples.