So God created man in his own image, in the image of God he created him; male and female he created them.
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. Then the man said, "This at last is bone of my bones and flesh of my flesh; she shall be called Woman, because she was taken out of Man."
The Claim: Genesis 1 says that man and woman were created at the same time, whereas Genesis 2 clearly says that man was created before woman. Which one is correct?
The Explanation: To answer the question, man was created before woman, and both passages support this. Since the claim admits that Genesis 2 supports man being created before woman, we only need to analyze Genesis 1. To do this, we'll analyze Genesis 1:27 by breaking it down into smaller pieces.
So God created man in his own image,
Notice it says "God created man," and not, "God created man AND WOMAN." So far, this supports the idea of man coming before woman.
in the image of God he created him
Once again, it says God created him, it doesn't say God created him and her. This still supports man being created before woman.
; male and female he created them.
Notice the semicolon here. A semicolon indicates that we can separate the two ideas into two separate sentences. If we did, it would look something like this:
So God created man in his own image, in the image of God he created him. God created male and female.
Genesis chapter 2 simply goes into more detail about the events in Genesis chapter 1. Therefore, you can take the details of Genesis 2:21-23 and place them between those two sentences, right where the semicolon is.
Both passages support man being created before woman, therefore, there's no contradiction.