Everyone around her had known the real situation and had lied to her except Spike. She only found out by sneaking into The Magic Box and reading the notes Giles had made. Her reaction was perfectly justifiable. We see her find out:
SPIKE: (frowns at book) "The monks possessed the ability to transform energy, bend reality." Blah, blah, blah. (looks at Dawn) Good lord, Giles writes as dull as he talks, doesn't he? (back to book) "They started work. But the Council ... has suggested ... to us that they were interrupted. Presumably by ... Glory." (Dawn continues staring into the distance as she listens) "They obviously did manage to accomplish the taste..." (looks closer) "accomplish the task. They had to be certain the Slayer would protect it with her life. So they sent the key to her ... in human form. In the form of a sister."
Zoom in on Dawn's shocked expression.
Spike frowns, looks over at her.
SPIKE: Huh! I guess that's you, nibblet.
When the only honest person in your life is a vampire, you need new people. Later on, Dawn's reaction is not healthy:
We see Dawn standing in the doorway. A large knife in one hand, blood running down her other arm from a wound across the inner forearm.
DAWN: (dazed) Is this blood?
We see Joyce and Giles across the room, turning to look.
BUFFY: Dawn!
JOYCE: Oh, baby.
Buffy and Joyce rush over to Dawn.
BUFFY: What did you do?!
DAWN: This is blood, isn't it? It can't be me. I'm not a key. (Buffy looks shocked) I'm not a thing.
JOYCE: Oh, sweetie, no. Wha-what is this all about?
DAWN: (grimly) What am I? (getting teary) Am I real? Am I anything?
She begins to cry. Joyce hugs her. Buffy watches grimly, also a little teary-eyed.
Then the lame excuses begin:
DAWN: (softly, not looking up) Why didn't you tell me?
Joyce looks at Buffy.
BUFFY: We were going to. It just... (trails off. Dawn gives her an angry look)
JOYCE: We thought it would be better if we waited until you were older.
DAWN: How old am I now?
JOYCE: You're fourteen, sweetheart, you know that.
DAWN: No. The monks. When did ... when did they ... (trails off)
BUFFY: Six months ago.
DAWN: (trying to hold back tears) I've only been alive for six months, huh?
JOYCE: Honey, you've been alive a lot longer than that to us.
DAWN: You don't know that! You don't know anything. I'm, I'm just a key, right? Everything about me is made up.
BUFFY: Dawn ... (sits on the bed next to Dawn) Mom and I know what we feel. I know I care about you. I know that I worry about you-
DAWN: You worry about me because you have to. I'm your job. Protect the key, right?
BUFFY: I worry because my sister is cutting herself!
DAWN: Yeah? How do you know? Maybe this is just another fake memory from my fake family.
JOYCE: Sweetheart-
DAWN: Get out.
BUFFY: Dawn...
DAWN: Get out, get out, get out!
Well what did they expect? Lunatics had already told her, "You're not real" and "There's nobody in there" so it's not as if keeping it all in the family was keeping it safe. Buffy managed to kill the giant snake in "Shadow" who had found out but the secret was not going to be kept for long. It was going to come down to whether they could keep the secret long enough for Glory to miss her appointment with interdimensional destiny. Dawn (rhymes with "pawn") was not complaining about some boy not liking her or flunking a test, she was complaining that people kept vital secrets from her. That is justification enough.
When people lie to me, I usually cut them out of my life. If that is impossible, then someone tells me situation A has happened, I immediately ask myself what the real situation B is that would make the person try to convince me situation A had happened. I quietly write them off as reliable sources of information. Dawn was serving notice that this was how she viewed them and no words that came out of their mouths was to be trusted ever again. I am totally onside with Dawn in "Blood Ties".