Just where did the rabbis themselves determine the idea of instituting four cups of wine? The rabbis wrote these instructions in Tractate Pesachim during the time of Roman rule in Israel, and during that time it was customary at Roman feasts or banquets (known as symposiums (sym – together, posium – drinking wine)) to begin the festivities by drinking wine. This was followed by going into the dining hall and eating the main meal which was accompanied by more wine. At the end of the main meal, more wine would be served to the guests. The rabbis of Roman times in Israel added a fourth cup of wine - the kiddush cup - to sanctify God and His merciful deeds, which established the four cups of wine as mandatory for the Passover Seder: (1) the first cup of wine drunk for kiddush; (2) the second cup of wine drunk just before the main meal; (3) the third cup of wine drunk after the "Grace After Meals" ritual; and (4) the fourth cup of wine drunk after the conclusion of "Hallel" which is near the end of the Passover Seder.

What “proof text” did they use to make this ritual act “Jewish”?

“Therefore, say to the Israelites: ‘I am the Eternal, and I will bring you out from under the yoke of the Egyptians. I will free you from being slaves to them, and I will redeem you with an outstretched arm and with mighty acts of judgment.  I will take you as my own people, and I will be your God. (Exodus 6:6-7)

How Important are these Four Cups?

The Sages of the Talmud understood drinking four cups of wine at the Seder to be an expression of freedom, cherut (Talmud Pesachim 117b)
Even the very poor should demonstrate the symbols of redemption and freedom, by eating and drinking in a reclining position, and be provided with the four cups. (Talmud Pesachim 99b).
Wine also filled in for at least some of the joy of the missing paschal offering in the post-Temple era: “Now that the Temple no longer exists there is no rejoicing except with wine” (Pes. 109a). 
The abundance of wine at the Seder also reflects the general esteem in which the Rabbis held the fruit of the vine.  “A person in whose house wine does not flow like water has not reached the ultimate stage of blessedness!” (Eruvin 65a). 
A third-century text compares wine to aggadah – the beloved rabbinic art of telling stories and finding every new meaning in ancient texts – because both exert “a pull on one’s heart” (Midrash Sifre Deut. 317).  In rabbinic parlance, aggadah and haggadah are generally interchangeable.  Drinking wine provides the perfect accompaniment to exploring the Haggadah (literally, “telling”) as we celebrate z’man cheruteinu, “the time of our freedom.”  (David Arnow as found in My People’s Passover Haggadah, Jewish Lights Press)

The Metaphors of The Four Cups:

Whereas matzah's bland taste symbolized the hardships of slavery in Egypt, the rich and strong taste of wine corresponds to the richness and strength that the Hebrews felt once they stopped believing the idea of worshipping Egyptian idols and instead chose to worship G-d during their wanderings in the Sinai Desert after they left Egypt.

One tradition links each cup with one of the four matriarchs, Sarah, Rebekah, Rachel and Leah, who gave birth to the Jewish people.
The cup of kiddush (#1) stands for Sarah who was the mother of a community of converts, believers by choice.
The cup of maggid (#2) is for Rebecca who knew how to mother both Jacob and Esau, two opposed natures.
The cup of Blessing after Eating (#3) represents Rachel whose son Joseph provided the whole family of Jacob with bread in time of great famine.
The Cup of Hallel (Praise) (#4) is for Leah, the first woman to praise God (Genesis 29:35)  -
based on teachings by the Maharal of Prague (famous for the legend of the Golem) and Rav Isaiah Horowitz of Tsfat (16th c)

The cups can be connected with the natural elements: earth, air, fire, water, to remind us that true liberation happens when our lives are in harmony.

Why is wine a promise of freedom?  When people count sufficient seasons of pure settlement to plant, harvest, press and age this sweet liquid, we taste freedom.

haggadah Section: Kadesh
Source: My People’s Passover Haggadah, Jewish Lights Press