If Eve is made from Adams rib, all humans would have the same genetic structure
Now, if Eve were made out of Adam's rib, it would seem that Eve is a clone of Adam. Since these two were the parents of all mankind, and they had the same genetic structure, then there is absolutely no way to account for the wide range of genetic diversity present in the human race.
Even if you were to concede that Adam's rib only played a small part in Eve's make up, and she had her own genetic structure, with different DNA, the union of only two individuals to form all of mankind [only 6,000 years ago] would still lead to a very limited genetic diversity (unless of course you allow mutations to play a role to diversify our genetic structure - but then, if you do, you have let in - dare I say it? - evolution).