Does Genesis 1 & 2 Contradict?

According to some skeptics, the Bible is contradicting itself in these two chapters over what God had created. In Genesis 1:25-27(read below) God creates animals before creating humans; however, in Genesis 2:18-19, it seems as though God creates humans before creating animals.

Genesis 1:25-27

"And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good. And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. So God created man in his own image, in the image of God created he him; male and female created he them," (Genesis 1:25-27 KJV).

Genesis 2:18-19

"And the Lord God said, It is not good that the man should be alone; I will make him an help meet for him. And out of the ground the Lord God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof," (Genesis 2:18-19 KJV).

In Genesis 1, we see a rough explanation of what had occurred; however, what do we see in Genesis 2? Well, we see many things, it is far less vague for this is the point of Genesis 2. Genesis 1 was a broad stroke while Genesis 2 goes further into the specifics. The Bible is not claiming there was a different order; rather, the text is clarifying the point of the animals. The Bible is not reclaiming the animals were made; instead, it is showing their purpose in relation to creation. The animals came out to give Adam a job. To further this point, the Hebrew word used in this passage for formed is "וַיִּיצֶר֩" which is a past tense word; thus, God had made the animals before this point in time.