
There is no secret: Dawn is annoying. People don’t like her. She’s an annoying character, an annoying story devise, an annoying sister.
(Background for the uninitiated or forgetful: Dawn is Buffy the Vampire Slayer’s little sister. She is introduced in season 5 by magic and retroactively fit into everyone’s memories. She acts like a very annoying brat of a child despite being only a year younger than Buffy was at the start of the series)
Here’s my guess (aside from the crazy cheat of why she exists) about why she is SO ANNOYING: She is characterized as a stereotypically immature teenager. She is exactly the opposite of what this show does great, which is to treat teenagers (of Buffy’s age) with respect.
Because Buffy and the Scoobies are not mature, parent-aged adults even while they are forced to act as parents to Dawn, a distance must be created between their world and Dawn’s. Their world is so completely Young Adult – despite their magic ability to buy alcohol in public at the ripe old age of 19 (which would be fine if the series took place in Canada, but it doesn’t.)

So putting a gap between Dawn’s teen angst and the Scoobies’ YA angst makes Dawn SO FREAKING DUMB. She is whiny and self-involved to the extent that she gets angry when people treat her with maturity and even angrier when they don’t. She throws tantrums and then accuses them of treating her like a child. She complains that she doesn’t get enough attention and then runs away as soon as the conversation goes in a direction she disagrees with.
Dawn’s terrible behaviour is explained as “teen” but it’s not – not in the Buffyverse. Not in the way that Buffy and Xander and Willow were teens a mere four years prior. We had three solid years of great teen storytelling and never were any of Buffy’s peers as awful and immature as Dawn.

Dawn is a child (like a 6 year old child) in a 14-15 year old’s body, because Buffy is forced to act the parent as a 19-20 year old. For some reason, the show doesn’t seem to want Buffy and Dawn to be peers. Dawn is not allowed to have the same kind of drama that Buffy experiences: boy drama, identity drama, friendship drama. So instead, Dawn is reduced to petulance and the most annoying trappings of “youth.”
It’s particularly frustrating in the context of this amazing show that does amazing things with representing the serious reality of adolescence and burgeoning adulthood. If Dawn were a character of any other television show, that show would be slammed for its careless and disrespectful representation of teenage stereotypes. As it is, it’s hard to pinpoint why she’s the worst because no one expects such a smart show to make such a faux pas.
Conclusion: Dawn is annoying.