In terms of Public Policy, you should consider comparing the Carbon Tax with the taxes on Tobacco.
Initially the negative health impact of smoking was not recognised. When the first research emerged relating smoking with serious diseases such as cancer the big Tobacco companies resisted this and tried to discredit the research.
Eventually the government recognised the negative health impacts of smoking and took steps to discourage smoking, such as restricting access to tobacco to minors and adding taxes.
Taxing something makes it more expensive and will directly reduce it's demand.
I don't recall what happened at the time, but I imagine smokers complained about the cost and how it was impinging on their ability to enjoy smoking.
This approach worked, and the levels of tobacco consumption have been falling in Australia for decades.
I don't think any rational person would argue about the idea of discouraging tobacco consumption, although assuming rationality in anonymous internet forums may be futile.
Climate change is a scientifically proven fact, backed by more than two decades of peer-reviewed academic research.
Reducing carbon emissions should help to mitigate climate change.
Putting a tax on carbon should reduce carbon emissions by making it more expensive and encouraging alternatives.
Looking back now, we can say public policy decisions made decades ago to reduce tobacco consumption were obvious and wide.
I suggest that, while not everyone will agree now, in decades to come taxing carbon emissions to reduce the pressure on global warming will be viewed in a similar light.