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The creation story in Genesis 1:1-2:4a is written in a different style than the more primitive creation story in Genesis 2:4b-25. The first creation story is consistent in style and language with other passages attributed to the Priestly Source, and is therefore also attributed to the same source. The second creation story is consistent in style and language with other passages attributed to the anonymous source now known as the Yahwist. Although the documentary hypothesis is no longer considered as simple and straight-forward an explanation of the development of the Pentateuch as it was once believed, in one form or another the hypothesis remains the best explanation we have.
Leon R. Kass says in The Beginning of Wisdom: Reading Genesis, at page 56, that once we recognise the independence of the two creation stories, we are compelled to adopt a critical principle of reading if we mean to understand each story on its own terms. We must scrupulously avoid reading into the second story any facts or notions taken from the first, and vice versa.
In the first story, animals are created before man and in the second story, the man is created before the animals. As Kass has inferred, this should not be seen as a contradiction, but the inevitable result of two different stories being written by two different authors. There is no need to regard either one as more correct than the other.
Upvote:3
In verse 19, it also talks about how formed the fowls of the air, while in chapter one, it says that they were created on day 5, a day before man. Therefore, it can be inferred that that there is shift between verses 18 and 19, while it goes back in time a little to give a better understanding of how he noticed that he needed one. While the first chapter was about detailing what happened in what order over the course of days, chapter two is much more detailed, but not entirely chronological. Also, since Eve was made from a rib taken from Adam after he noticed his lack of a female counterpart, she was obviously made after.
Upvote:11
In order to understand the meaning of any text, you must understand it's purpose. If you don't understand why a bit of text was written, you are quite likely to come away with a bad understanding of what it means.
In this case your question assumes a mis-understanding of the purpose of the two texts in question. If you correct that understanding, it becomes apparent that there is actually no contradiction and nothing that needs resolving from an inerrancy standpoint.
The two chapters you quote from in Genesis serve slightly different purposes. It is quite common on ancient Hebrew literature to repeat parts of a story in different ways to draw out different points. In this case one passage tells us something about the Chronology of events, the second goes on to give us another event that happens to be sandwiched inbetween the last steps of the first event that includes some additional commentary.
If you want to know in what order things were created, Genesis 1 should be your guide.
In Genesis 2, we find out that that (presumably about day 6) God was trying to show Adam that his own personal help-mate was going to be a different kind of creature than the animals, so after he makes Adam but before he makes Eve he parades the rest of the created order before Adam and demonstrates that none of them are like he is. The animals are not made on the spot, there is just a bit of commentary that reminds us that they were created out of the ground. In the process, all the animals get names.
But then we go on to the creation of Eve, made not out of the ground but out of Adam's flesh. This second chapter helps us establish some order or rank to creation as well as lay the foundation for its purpose, not re-sequence the events of creation.