Midrash Morsels on Lech Lecha
However, this translation is incorrect according to Bereishit Rabbah. Rather, it means that Avraham Avinu told Lot, "Whichever way you go, you will be to my left. If you go left, I will go right. If I go right, you will go left."הֲלֹא כָל-הָאָרֶץ לְפָנֶיךָ, הִפָּרֶד נָא מֵעָלָי: אִם-הַשְּׂמֹאל וְאֵימִנָה, וְאִם-הַיָּמִין וְאַשְׂמְאִילָהIs not the whole land before thee? separate thyself, I pray thee, from me; if thou wilt take the left hand, then I will go to the right; or if thou take the right hand, then I will go to the left.
In the Sod of the matter, explains the Nezer Hakodesh, the left refers to the female aspect. When Avraham and Lot were together, Lot had the same amount of holiness as Avraham. When Lot separated himself from Avraham, however, 99% of his holiness left him - only a few sparks on the left remained. Because of this, the halacha of מואבי ולא מואביה was enacted, as only the female side of Lot had some holiness. And we see this from Rut and Na'ama Ha'amonit, 2 women who would be great-great-...-grandmothers of Mashiah.
But what started the argument in the first place? Avraham's animals were muzzled, while Lot's were not. Lot claimed that he could keep the animals unmuzzled since the land belonged to him since he would inherit from Avraham since Avraham had no children at that point. The verse therefore shows the error of Lot by concluding that the Canaanites were still in the land to show that Avraham had not yet gotten the go-ahead to inherit the land.
Later on, Avraham complained to Hashem that Lot would be his inheritor (according to Ribbi Elazar). Hashem answered him that Lot would not be his inheritor as Lot Lita (Lot's name means "cursed" in Aramaic).
Rather, he would have a son and when a son exists, the female side doesn't inherit.
According to the Nezer Hakodesh, when Hashem said Yado'a Teda, Hashem was in essence telling Avraham about the Final Redemption. We see this because the Midrash says "Yado'a that He will scatter them - Teda that He will gather them." In Egypt, we were not scattered. This proves that it refers to the Final Redemption. Also, the Midrash talks about the 4 Malchuyot when discussing the previous verse and the next verse.
According to this, Avraham Avinu asked "Bameh Eida" - meaning, "How do I know that my children will inherit the Eretz Hahayim in the Future Redemption and not be destroyed by the exile?" Not that Avraham Avinu ח"ו had a lack of faith in Hashem, but he was afraid that that maybe his children would give up hope from being redeemed and remove the yoke of Torah which will inevitably cause them to lose their merit of receiving the Eretz Hahayim as an eternal reward.
On this, Hashem answered him that the redemption from Egypt will be signs and wonders for the Future Redemption since כימי צאתכם מארץ מצרים אראנו נפלאות so they will never give up hope. However, it could be that even without the signs and wonders, we would have believed in the Future Redemption since we are believers - children of believers. However, because Avraham Avinu opened his mouth to the Satan and said "Bameh Eida" because maybe we would not believe in the Redemption, Hashem had to make a sign and wonder, and it unfortunately needed to be preceeded by the Egyptian exile.