If you look at the verse from the perspective that it cannot contradict, then the same verse can be read without incorporating a new chronology into it.
Genesis 1 has already given us the chronology. What is the purpose of interpreting it in such a way that it would be contradictory?
What way
is there to interpret Genesis 2:19 so that it does not contradict the earlier chronology? It specifically states that Adam was already there to see and name the birds when they were made.
Reasoning and interpreting is a very good thing... but you need to let us know what this other interpretation is, and how it can be reconciled with the text.
"If I had to write ten jokes about potholders, I don't think I could do it. But I could write ten jokes about Catholicism in the next twenty minutes. I guess I'm drawn to religion because I can be provocative without harming something people
really care about, like their cars."
-George Meyer,
Simpsons writer
™ Version 4.2