Your furnace is big. Little things give us little problems. Big things give us big problems. It's not such a hard concept to grasp. Lacking enough oxygen, however, you get carbon monoxide, with only one atom of oxygen per atom of carbon.
Carbon dioxide is harmless.
Carbon monoxide will kill you. A gas range typically uses 10,000-15,000 BTUs of energy per hour. Most houses are sufficiently leaky that ample fresh oxygen can be drawn from outside to replace what's lost to combustion. Not so with a furnace, which can use 100,000 BTUs or more. If the furnace isn't vented or if the vent is blocked, the oxygen supply is quickly depleted, resulting in lots of carbon monoxide and a bunch of asphyxiated folks.