Giants are also a symbol of arrogance, while our forefathers, buried in Hebron, are a symbol of humility. Abraham stated to G-d, "I am but dust and ashes." When we nullify the chametz, we pronounce, let it be considered "like the dust of the earth."
The four giants/exiles also appear to parallel the four couples. Sheshai/Babylonia (Bavel), is reminiscent of the Tower of Babel, a generation which Avraham had to confront directly - particularly its leader, Nimrod. Avraham is also known for destroying the statues of his father.
Achiman/Persia is an exile and the Purim story are characterized by extreme self-sacrifice, a characteristic of Isaac and theAkeidah, as we saw last week. The Torah also makes references to how Isaac and Rebecca prayed together for a child, and how much of what happened to Isaac and future generations were actually determined by Rebecca's actions, such as the blessing of Jacob over Eisau.
Talmai/Greece was primarily about an affront to the Torah, its Divine origin, and its lifestyle. Torah is mainly a characteristic of Jacob. Jacob, Ish Tam (a wholesome, "simple/straightforward" man) stands in contrast to the godless (or pantheistic) "sophistication" of the Greeks.
The father of the giants/Rome, involves all of humanity. Pax Romana reached the entire world, and in many ways we are still under it today. Edom is Eisav, who was red, also symbolic of Mars and of his military prowess. Adam and Eve represent all of humanity, yet Adam is also an acronym of three people: Adam (himself), David, and Mashiach. David was also red. He was a "kosher" version of Eisav and of the potential that he so badly missed. Mashiach son of David, will come and redeem the entire world, fixing the curse of the snake, and bringing the world back to its fullness and potential, like that of Adam and Eve in the Garden of Eden.