Genèse 15:10

And he brought all these before Him, and divided them in the midst, and set in order every division over against its fellow; but the fowl he divided not.

AND HE DIVIDED THEM IN THE MIDST. This he did in order that He make the covenant with him, to pass between these parts.
He thereby alluded to Abraham that all sacrifices of cattle and fowl will be from these species since the gozeil (young pigeon) mentioned here is identical with the ben yonah (young pigeon) mentioned in the Book of Leviticus. Here it is called gozeil to indicate that only the young of this specie are fit for sacrifices. Now even though all young fowl are called gozlim — as it is said, As an eagle that stirreth up her nest, hovereth over ‘gozalav’ (his young ones) — Abraham understood on his own that the command of the Eternal applied to the kind which was to be selected [by the Torah, namely, young pigeons]. It may be that Abraham followed his own will in offering a young pigeon, and Scripture selected forever the specie which the patriarch had offered.
Thus did Abraham know that the sacrifices would be of these species and that all of them would be divided into parts: the Whole-offering into its pieces, the Peace-offering into the breast, shoulder and fats,, 7:30-32 and the Sin-offering and the Guilt-offering into their fats., 4:31; 7:2-5.

BUT THE BIRD HE DID NOT SPLIT. He placed the turtle-dove and the young pigeon opposite each other for they too were in the covenant, but Abraham did not split them in the middle since concerning all fowl offered on the altar it says, He shall not separate it., 1:17. In Bereshith Rabbah the Sages said, “The Holy One, blessed be He, indicated to him that in a bird Whole-offering, the ministering-priest severs both the gullet and the windpipe, but in a bird Sin-offering he does not sever” [the head from the body, as he must cut one and not both of the organs]. [hatzipor — singular] he did not split? This is to indicate that of the two kinds of sacrifices to be brought from fowl, namely, the Sin-offering and the Whole-offering, only one would be subject to the injunction not to separate it, and Scripture later specifies that this is the bird Sin-offering. (Leviticus 5:8.)

ויבתר אותם בתוך, both what he cut in half and what he did not cut was at the command of G’d, even though the Torah did not mention this specifically, The reason for cutting something in half was to show that G’d was making a covenant with Avram, as we already explained on verse 9. G’d hinted to Avram, by means of these carcasses being cut in half, that all the nations exiling the Jewish people, would suffer a fate as that suffered by these sacrificial animals. They would successively fight wars, the younger one against the older one, one wiping out the other eventually. All those nations represented different cultures, both in their secular outlook as well as in their religious orientation. All of this would be caused due their competitive spirit, each nation trying to achieve dominance over the others. Such behaviour is not typical of the Jewish people, although, for a brief period in our history, the tribe of Ephrayim competed violently with the tribe of Yehudah for pre-eminence among the 12 tribes of the Jewish people. Even during such periods, these tribes would not remain divided culturally or religiously. (compare Isaiah 11,13) אפרים לא יקנא את יהודה ויהודה לא יצר את אפרים, “Ephrayim will not be jealous of Yehudah, nor will Yehudah oppress Ephrayim.” To signify this difference between competition among the gentile nations, and tribal warfare in Israel, G’d told Avram not to cut the bird in half, seeing that it represented the nation that would emerge with Avram as their founding father. Therefore, the Torah reported ואת הצפור לא בתר, that Avram did not cut the bird in half. The word הצפור includes both the pigeon and the turtle dove, תור וגוזל, seeing that the Jewish people are scattered in the four directions of the globe and have yet remained a single people, clinging to their Torah and their faith in spite of being scattered all over the world. The people of Israel did not trade their religion for another in spite of the heavy burden involved in enduring exile.