Qerev is the essence of membership, as pesach is the essence of strangership.
Each member gets a share of a kill. As such, animals as food differ from fruits and vegetables as food, since vegetables come in quantities more easily personalized to the individual consumer. Animals, in contrast, require co-operation for the kill and animals also produce an excess of meat once their having been killed.
The zevach pesach defines the lamb or kid as the basic consumption unit because it typically extends the unit of consumption beyond not only the individual to the family, it also extends beyond the family to the clan or the neighborhood.
The qorban delivers to God His portion of the animal so that God may join as a member of the people.