Bo: Meshech Chochmah and Chizkuni: Mitzvah 14 – Concept 417
You shall not leave any of it until morning.” (Exodus 12:10) We are prohibited from leaving any of the meat of the Pesach offering over until the morning. (Rambam, Hilchot Korban Pesach)
They ate the animal only after it was well-cooked with patience, yet, they also ate as if prepared to rush out at any moment; their staffs and bundles were ready for an immediate trip. They understood that they would be rushed out of Egypt in a spectacular manner.
They were combining patience with a sense of expectation and excitement.
However, with Chatzot, midnight, and the beginning of the Slaying of the First Born, they were surviving through a miracle that was the beginning of their exodus,(Meshech Chochmah) and people who are about to leave on a trip do not leave food over. (Chizkuni)
They were given an opportunity to taste the freedom they would experience in order to live with that expectation. However, we eat the Pesach offering with a sense that we are about to begin an entirely new journey in life, and cannot take certain things with us into the future.