When I've heard it, at several workplaces (decades ago), the stated objective was always to be the pig-- to go "all in." The chicken was involved, the pig was committed-- thus we are asking you to be committed.
Usually, after the meeting, a few of us would quietly point out that the pig was eaten, and they were asking us to sacrifice ourselves to the project, but that never seemed to discourage the metaphor from coming up, again and again.
Usually, after the meeting, a few of us would quietly point out that the pig was eaten, and they were asking us to sacrifice ourselves to the project, but that never seemed to discourage the metaphor from coming up, again and again.