A very common claim from Atheists or other critics of the Bible is that Genesis 1 and 2 present two completely separate creation accounts, which contradict one another many times.
This, in my opinion, falls into the "bad reading comprehension" category of alleged contradictions, as the two chapters, and how they fit together, are really not that hard to understand.
But wait! Haven't you noticed?
In chapter 1, God makes animals, then people (Genesis 1:20-25), but in chapter 2 it says God made man (Genesis 2:7) then animals (Genesis 2:19), then woman (Genesis 2:21-23). Also, we were told that the birds were made from water in Genesis 1:21, but chapter 2 says they were made from ground (Genesis 2:19). And we are told that the fruit trees were made 3 days before man (Genesis 1:11-13), but later we are told that they were made with man (Genesis 2:9).
I implore you to read the two chapters, without any interruption or commentary. When you do, it becomes obvious that Genesis 2 covers the events on day 6 when God made mankind (Genesis 1:26-27), specifically in the Garden of Eden:
Genesis 2:7-8
7 And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
8 And the Lord God planted a garden eastward in Eden; and there he put the man whom he had formed.
Genesis 1:1 - Genesis 2:3 is a brief summary of the entire creation account. The rest of chapter 2 is where we get more details on day 6, where God formed another of each animal in the Garden of Eden for the purpose of Adam to name them, before God made Eve.