A friend, Des Jones, points out that in the proto-Exodus stories in Genesis the threat is to the bride and therefore it is an attack on the children of the covenant promised to Abraham. Pharaoh and Abimelech are implicitly co-opting the the “seed” of the woman. And this becomes explicit in the Exodus narrative when Pharaoh orders the murder of the baby boys but explicitly orders the sparing of the daughters of the Israelites. Why keep the daughters alive? Because they are the future brides of Egyptian sons. The Pharaoh knows that cultures are ultimately built on people and their children.
But Yahweh knows this as well, and so when He comes to deliver His people, He strikes down the firstborn sons of Egypt. To strike down the firstborn sons is not merely retribution for the murdered Israelite sons, it is to strike down the virility of Egypt, their potential to raise up a new generation of Egyptians. The firstborn sons are the “leaven” of the culture, the strength of the culture, the evidence of a new generation on the rise.
Therefore Israel must rid themselves of all the leaven of Egypt while striking their houses with the blood of the Passover lamb. If anyone eats anything with leaven in it, that soul will be “cut off.” In other words, to eat the leaven of Egypt is to be aligned with the Egyptian firstborn and come under their judgment. But to get rid of the leaven is to renounce Egypt and his strength. It is to reject Egypt as a false husband and to look to Yahweh as the true husband, the only source of life.