Invictus,
If there are animals before man, then when God puts man in Eden, he would not be alone. Further more, God would not have created all the animals if they already existed.
Don't you think that this is a superficial understanding of God mentioning that it was not good for man to be alone? God's mentioning that it was not good for the man to be alone was in anticipation that He would build for Him a wife. I don't think that God meant that it was a good idea for man to have a animal companion.
God's bringing the animals to man to name was not for God's sake. It was for the man's sake. It cultivated within the man a sense of his uniqueness and prepared him for his wife, a true helpmeet and counterpart.
Gen 2 wouldn't mention the creation of the animals before mentioning the creation of man, because the people who wrote Gen 2 were under the impression that man was created first.
I don't know that. Maybe that was an impression and maybe is was not. And if it is there is little effect on the account. Both Genesis 1 and 2 show man at the pinnacle of created lives on the earth. One may be clearer about man being created after all the animals than the other. But both place man at the philosophical apex of all created lives on the earth. The only exception being the tree of life and God Himself.
In both chapters we ascend up the ladder of the significance of living creatures and find human beings at the apex.
They are simply using a chronological ordering of the events (which is logical), and so mentioning something that happened after event 'A' before mentioning event 'A' would simply be confusing and illogical.
There are other explanations possible. Chapter 2 may be more local to the garden in Eden. I think Adam must have been the originator of one of the accounts. One of the accounts may have been passed down from the first humans created, the original ancestors of which would have been Adam and Eve.