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In most tissues, there is a 5% CO2 level. Or at least that is the level of CO2 required to grow human, bird, mouse cells in culture. CO2 in itself is not toxic. You die in 100% co2 because you suffocate when O2 is displaced as it sinks in a closed container. It is CO that competitively binds to hemoglobin over O2 if I remember right.
Oxygen and CO2 binding to hemoglobin largely depends on the Oxygenhemoglobin dissociation curve, which determines the hemoglobin's affinity for them and other substances (like how carbon monoxide binds more readily to hemoglobin than oxygen by over 200 times!). The resulting shift to the left or right causes alkalosis or acidosis.
The problem with using CO2 for culling is because the chemoreceptors that detect levels of carbon dioxide. The body knows when it is suddenly experiencing hypercapnic hypoxia (high CO2, low O2), and triggers a panic response that includes hyperventilation in an attempt to correct the situation. The animal will lose consciousness eventually, but such a death isn't pain free, if you can imagine the sensation of not being able to breathe.