Earlier quoted context omitted.
In order to be politically acceptable, a carbon tax should be phased in gradually and coupled with a reduction in income tax so as to make it revenue neutral. That way it can't be framed as just another government tax grab.
Offsetting income tax would be a massive handout to the rich, who have been and continue to be the greatest contributors to carbon emissions. Instead, it should be paired with a dividend which makes it revenue neutral for the median household. Lower income families, who are more impacted by but less responsible for climate change, would be paid a benefit.
I'm not sure how these two ideas make sense in your head. If you implement a carbon tax and the rich are the greatest contributors as you stated, one would expect them to be hit by the carbon tax as well.
In any case, I personally see an income tax as a strange thing to have in the context of a discussion wherein taxing undesirable behavior is seen as a way of disincentivizing it.
At the very minimum free the working class and lower-middle class from income tax.