It's more of a fee for polluting the atmosphere with your CO2. The atmosphere is public space. If you don't want to pay a tax, design a mechanism to capture all the CO2 you release, and store it in a warehouse.
If I went and started dumping waste from a septic tank on a public park, then i'd get fined, and probably some more severe penalties.
Who gets that fee for polluting the atmosphere? Why should they have it? What do they do with the trillions of dollars? Surely they should be inventing a CO2 capturing machine with all that money? But they don't.
Dumping septic waste is demonstrably hazardous to other people's health. CO2 in the air is not. I breath out CO2. Should I pay for breathing?
The CO2 you breath out is being liberated due to cellular respiration, and that liberated CO2 is equivalent to the amount of CO2 that was sequestered by the plants that eventually provided you energy. Therefore the short-term (lets say 100 years) output is 0. The net output
If you'd like to see the negative health effects of CO2, try breathing out of your cars exhaust (don't actually do this). (Granted this is not a great example since you'd basically be depriving yourself of oxygen. However, increased CO2 in the body can lead to more acidic pH levels in the body, which is hazardous.)
Combustion engines will also produce carbon monoxide, which is poisonous to humans(and many other things).
Combustion engines will also produce nitrogen oxides, which will be created from the reaction of oxygen radicals produced from the combustion engine with nitrogen in the air, which has been shown to cause increased illness, and can lead to premature death from disorders of the lungs and the heart.
Nitrogen oxides are also fundamental in the production of acid rain, which is fundamental in the creation of acid rain and the acidification of the surrounding environment, which can kill off local animals due to pH intolerances.