The analysis of creation days in Genesis 1 that I find most persuasive is the one that claims that they are meant to be understood as a thematic rather than a chronological arrangement. It works like this: on days one, two and three God creates
1. Light
2. Sky that separates water above (rain) from water below (seas).
3. Land with vegetation.
But the light, sky and land of the first three days are "empty" or "unstructured". See verse 2: the earth was "without form and void", or "formless and empty". It was like a house that has no furniture, appliances, utensils, electricity, plumbing or people - a house but not a home.
The point is that God did not make a fully functioning world all at once. He did it in stages. First he established the superstructure, and then he filled it up and made it work. Notice how creation on the fourth, fifth and sixth days parallels the first, second and third:
4. Sun, moon, and stars
5. Fish and birds
6. Land animals
On the first day there was light, but now on the fourth day that light is fashioned into sun, moon and stars - lights that mean something to us and that we can use to mark days and seasons, and from which we can get our sense of direction. It is no longer "light" in the abstract but structured light that gives us a sense of time and place. On the second day God creates sky that separates clouds above from seas below - but it is an empty sky and a barren sea. Now on the fifth day God fills the sky with birds and the sea with fish. On the third day God creates dry land, but there are no animals on it. There is vegetation but no gardens; there is nothing to eat the vegetation or make any use of it. But on the sixth day God fills the dry land with land animals, and then finally makes man to govern all of it. Now at last the "formless and void" world has structure and meaning. The light has sun and moon, the sky has birds, the sea has fish, and the land has animals governed by man.
Understanding the material as thematically rather than chronologically arranged neatly solves a problem in verse 16. How in the world can you have "evening and morning, the first day" (and second, and third) if the sun does not even get created until the fourth day? I deny that a strict chronological interpretation can adequately comprehend that sequence. But if instead we are talking about themes presented under the organizing structure of two sets of three parallel days, then it makes perfect sense. The sun fills and completes "light" just as birds fill and complete the sky, just as fish fill and complete the sea, and just as animals fill and complete land. The author is not telling you when or how these things were created but what function they fulfill in God's creation.
This understanding also provides a ready explanation for why birds and fish were created "before" land animals. Why not some other order? Why not fish on day five and birds and land animals on day six? Or why not land animals and fish on day five and birds on day six? The reason is very simple. Birds and fish on day five have to match up with sea and sky on day two, and land animals on day six have to match up with land on day three. Again, the organizing principle is not chronological order but theme.
One of the things that the Genesis creation account is doing is decisively rejecting the creation stories of all other ancient cultures and religions. In those stories, gods created the world out of existing materials. But in Genesis, God not only fashions a functioning, living world - he even makes the raw materials for it in the first place. That is, he does not fill up a pre-existing structure, he makes the structure itself from nothing by the mere power of his Word. As a teacher of mine liked to say, "God speaks, and worlds leap into being."