I agree with [MENTION=10426]janas[/MENTION] SO much.
Dawn is Buffy's humanity. If she dies, so does Buffy, at least emotionally. If there's no Dawn, Buffy has nothing left to fight for because she has nothing left to lose.
'Chosen' was supposed to be a hopeful ending, showing Buffy that, yes, there is life after Sunnydale, there are others out there like her, she's free to be who she wants. Of course, the comics pissed all over that, but that's not the point. If Dawn had died in the school, that hopefulness is taken away, Buffy would be done, she'd have nothing left because Dawn - as was shown a lot in the show - is her everything.
Also, using Anya's death as 'proof' that Dawn should have also died is wrong, in my opinion. Anya might have been a thousand years old and had the experience of fighting as a demon, but she was completely human in this episode and she also didn't have eyes in the back of her head. She was taken by surprise, run though by a blade from behind by an attacker that she didn't and couldn't have seen coming. It's happened to the best fighters in this verse over the course of the eight TV years, including Buffy herself, more than once. In fact, it happened to Buffy in this very episode. The Bringer was just lucky that it managed to deliver a fatal blow to Anya, whereas the Uber-Vamp missed anything vital when it came to Buffy. Skill and competency in fighting is completely nullified when a fighter is taken by surprise from behind by an attacker they couldn't see.
There were other humans in this episode who also should have died if this is the criteria we're using, namely Xander and Andrew. Just because the three of them were lucky and skilled enough escape with their lives doesn't mean that that's 'wrong'.
Also, we've seen Dawn fighting before. She's not incompetent. She's actually very skillful and knowledgeable. She was able to study Buffy's moves and mimic her exactly, minus the skill and strength Buffy has because she's a Slayer. Dawn had been training with Buffy for months, before that was knocked on the head thanks to the Potential problem. She's not weak.