Oh, your questions!

Okay friends, at yesterday's "Breaking Open the Word" session, there were some questions about our first reading, Genesis 15: 5-12, 17-18; Why those particular animals to be sacrificed? Why three-years old? Why weren't the birds cut up? Excellent questions, since if such detail was given, it had to be significant, right? Well, my usual trusty resources weren't of a lot of help, but let's see what we can do....

Three years was considered the ritual age of maturity for these animals, so it was a sacrifice of an animal that was just reaching its productive or reproductive age (giving up something just as it was about to be able to repay your investment in it). Three is also a number representing perfection (think: Trinity).

The first answer I can give you about why these particular animals (heifer, she-goat, ram, turtledove, pigeon) feels like circular reasoning to me: they are the animals listed for ritual sacrifice in the first few chapters of the Book of Leviticus, reflecting the traditions established hundreds of years later... but I wonder if they didn't look BACK to Abraham for the 'inspiration'!

So I went to the internet... and without being 100% certain of the validity of the sources, I found a densely written site on "early Jewish writings" that ascribe allegorical meanings to the animals to be sacrificed. Here's a very brief summary:
Heifer (cattle, ox) is connected with the earth (think: plowing)
She-Goat is associated with water (think: rushing, impetuous)
Ram (sheep) is associated with air ("violent and vivacious")
So we have basic elements of earthly nature represented here. (The explanation goes on that since earth and water are material things, they are given feminine properties, and air, wind is given masculine properties).
Then they explain that the birds represent the heavens:
Pigeons the planets (more familiar, nearer to us) and doves the 'fixed stars' (more solitary, remote).

From this explanation is seems that the choice of this list of animals represents God's intention to be all-encompassing, to leave nothing out in the promise-making. (The missing earthly element? Fire... God appears in that form to seal the covenant)

We already talked in our session how the ritual of splitting the animals in half was a way of saying 'may this happen to me if I don't live up to my end of the agreement'.

Now, why weren't the birds cut up? Well, they may actually have been cut, but not divided in two. And again, I've got to go to the sources of early Church fathers for their symbolic explanations:

The fathers of the Church saw a separation between carnal man and spiritual man in the symbolism of the cut and uncut animals. St. Augustine, Bishop of Hippo, wrote: And it is said, “But the birds divided he not,” because carnal people are divided among themselves. But those who are spiritual are not divided at all, whether they seclude themselves from the busy conversation of humankind, like the turtledove, or dwell among them, like the pigeon. For both birds are simple and harmless, signifying that even in the Israelite people, to which that land was to be given, there would be individuals who were children of the promise and heirs of the kingdom that is to remain in eternal felicity (City of God, 16.24; Ancient Christian Commentary on Scripture, vol. I, page 33). St. Caesarius, Bishop of Arles, had the same interpretation: “The birds,” says Scripture, “he did not cut in two.” Why is this, brothers? Because in the Church catholic (universal), carnal people are divided but spiritual people are not. And, as Scripture says, they are separated one against the other. Why are carnal people divided and set against each other? Because all wicked lovers of the world do not cease to have divisions and scandals among each other. For this reason they are divided since they are opposed to one another. However, the birds, that is, spiritual souls, are not divided. Why not? Because they have “one heart and one soul in the Lord.” [..]. For this reason Abraham divided those animals into two parts, but the birds he did not divide (Sermon on Genesis 82.2, quoting Acts 4:32; Ancient Christian Commentary on Scripture, vol. I, pages 33-34).

(apologies, I have lost track of the internet source for this quote)

You people keep me working hard. I like that. 

And if you've found a different or better explanation, please share!