You might have heard it different, but this is the way it was told
to me:

     First, a pop quiz: Who was the first woman in the world? You 
said 'Eve', right? Wrong. God made Adam and Lilith at the same time,
both from the still-warm clay of the new earth. Having sprung from 
non-existance to full awareness in an eyeblink, they stood there in
the garden of Eden, amazed.
     Lilith saw wonder in everything she saw, from the vastness of 
the sky to the simple perfection of blades of grass she stood on.
     Adam turned to Lilith, and, "Okay, bitch. Clean this place up,
and get me some dinner. I'm going to take a nap, and then name some
stuff."
     Lilith said,"Excuse me?"
     Adam sighed. "What, are you deaf, or just stupid? Get moving. 
I've got a lot to do. I can't waste my whole day micromanaging you."
     Lilith put her hands on her hips. "Wait. What gives you the 
right to tell me what to do in the first place?"
     Adam pointed to his penis, and said, "I've got this, and it says
I'm the boss."
     Lilith kneed Adam in the groin, pointed at her feet, and said, 
"Well, I've got these, and I'm going to see where they take me." And
she walked away.
     A few days later, God found Adam, dirty, cold, and hungry, 
cringing under a tree.
     "ADAM" God said, in all caps, "WHERE IS LILITH?"
     "I don't know." Adam whined. "She went away."
     "WHY DID SHE LEAVE?" asked God, even though he knew the answer,
being omnisciencent and all.
     "I don't know," Adam said, breaking into tears. "She was crazy
or something. I really think there was something wrong with her. I'm
lonely. Can I have another woman? Kind of like Lilith, but nicer?"
     God sighed, which sounds kind of like a really big airplane 
taking off, and said, "ALRIGHT, I"LL GIVE YOU ANOTHER WOMAN. BUT IF 
YOU SCREW UP AGAIN, I'LL MAKE YOU GAY."
     So God made Adam fall asleep, and created Eve from one of Adam's
ribs. Of course, she was a total feeb, and the two of them were 
terribly co-dependant.
     Lilith went on to seek out the secret places in the earth, and
became the first witch. According to some stories, she also mated with
animals, gave birth to monsters, and brought evil into the world. But 
I think those are rumours Adam made up to slander her. He was a real
dick.
     Anyway, that's the story, the way I heard it anyway. 

For more Lilith lore: