The main theory I have come across in relation to Lilith is about belief.  If a person believes the Bible is the word of God then it cannot be wrong.  So, if the Bible states in Gen 1:27:

 "So God created man in his own image, in the image of God he created him; male and female he created them," 

and then in Gen 2:7:

 "then the Lord God formed the man of dust from the ground and breathed into his nostrils the breath of life, and the man became a living creature," 

followed by Gen 2:21:

 "So the Lord God caused a deep sleep to fall upon the man, and while he slept took one of his ribs and closed up its place with flesh. And the rib that the Lord God had taken from the man he made into a woman and brought her to the man."

These passages contradict one another.  The first states man and woman being created together.  The second two have Adam being created first, followed by Eve.  If a person believes that the Bible is the word of God then both are correct.  So, to make them both correct there has to be a first woman followed by Eve.  Which is how the idea of Lilith came about - filling in the gaps to make both versions true.  If a person believes the Bible is the inspired word of God, written by men capable of error, there is no need for Lilith.