Rachel Elizabeth Dare was never like other girls.

i. A dreamlike castle.

Other girls - they dream about a beautiful shimmering-in-the-light castle, full of knights and princes and princesses, a balls room and servants that'd walk around and do what they just ask; too bad Rachel already have all that.
Rachel? She dreams about staying in her cave forever, never leaving Camp Half-Blood. She loves the kids, she loves the place, she loves the fact that it feels like home just as much it feels like home to the demigods. She belongs there. She can do whatever she wants, whenever she wants. Her cave is big and warm, with silk-curtains that covers the entrance. Her drawings are all over the place, and no overreacting dad can tell her that it's "Unacceptable, young lady". It already is her happy-place; her dreamlike castle.

ii. To be accepted in society.

Other girls - they dream about being popular, being loved, being accepted, being a princess that everybody adores. The want to feel desired, and that means they don't care what they do to get there.
Rachel? She doesn't give a damn. All she care about is other people; she want to help the world, she wants people to live as happily as they can – her stomach flips upside down when she thinks about people starving in the streets, and she couldn't care less if that means to skip on one of her father's 'blend in the society' evenings.

How can you think about blending in the society, when you don't care about the society itself at all?

iii. Appearance.

Other girls - they want to have silky blonde hair, and bright-big-blue-eyes, and long dark eyelashes. They want cream-colored smooth skin, and plump soft rose-like lips, and perfect thin body. They can die trying to get there, because if they won't be the perfect Barbie - then they don't worth anything, right?
Rachel isn't like that; she has thick red hair, and pale skin with hundreds of freckles. Yes, she's thin, but she's short with dark-green-almost-forest-brown eyes. She's not perfect by any mean.
Does she care? No. She'd rather be on cleaning duty at camp than wear the lip-gloss and eyeliner and all the makeup her father wants her to wear so she'd look like a 'proper lady'. She wears ripped jeans and T-shirts covered with paint splashes, and her hair is usually in a messy bun. Appearance isn't what matters - it's the inside.

iv. Prince Charming.

Other girls - they dream about a blonde, tall, broad-shoulders perfect guy. He would have blue sparkling eyes, and he'd be nice and funny and handsome and smart and sweet and romantic. He'd be perfect. He would come and save them from the evil wizard, or the boring life, or whatever it'd be, and he would come on a white horse and sweep them off their feet to the sunset.
Rachel thinks Prince Charming is stupid. Perfect is stupid; it's boring. All that Rachel wants is the dark-haired, olive-skinned, brown-eyed guy. You can say he's broad-shoulder and tall and a hero, but that's a minor detail. The thing about him is that he understands her. He makes her laugh, he makes her smile, he annoys her to death - which is funny, because he's no son of a king, he's the son of the Lord of the Death. She doesn't want him to sweep her off her feet - she wants him to stand in front of Apollo and fight for their love.
(To do that, of course, he has to firstly admit they have a love, and that's not going to be easy.)

v. Happily ever after.

Other girls always want the same, and that's no shocker. They want to live with the perfect guy in the perfect house with perfect kids, and they want to live in a fairytale that ends in a happily-ever-after ending.
Rachel doesn't really care. All she wants is to live. Really, truly, actually live. She regrets the stupid mistake she did when she was sixteen - she was heartbroken and thought the world will never be the same. She gave up on love, and a normal life. She wants to take that back.
It's not that she doesn't like being the Oracle, because she does. It feels right and all; but the price she has to sacrifice is too high. She wants to be able to have kids and a husband - especially that one half-Italian 20-years-old demigod - and she wants to be able to do whatever she wants and go crazy with no God of the Sun pushing her around. She wants to tell that stupid Italian demigod: "Hey! Idiot! I love you! Why are you so blind? As my best friend, you sure as hell don't know me as good as you think!" without having Apollo fry him. She doesn't want a happily-ever-after; she just wants the dark boy there, always by her side, annoying her forever and always.

There's one difference between Rachel's version of fairytale and other girls' version, though.
Rachel's one – well, it can actually come true. All she has to do is wait patiently for the next confused little girl that sees weird things, weird monsters, and weird world. She could then pass away her powers, and yell at the dark boy all she wants.

Who said fairytales don't come true?