All of those necessities get more expensive with a carbon tax, so we need a way to cushion the impact on those who struggle to pay for the basics.
While the impact of global warming does impact the global poor quite heavily (think of places like Bangladesh) it doesn't really hurt the poor in developed places much more than the rich in developed places. I was a lot less worried about El Niño when I rented an apartment, for example.
Because they need to spend more of their income in order to survive.
If you spend all of your income, a 10% sales tax reduces your income by 10%. If you only need to spend half of your income, a 10% sales tax reduces your income by 5% - or less, if the money you don't spend earns interest.
You're assuming here that the money will be spent on the poor, but we really have to make sure that will actulaly happen if we want the carbon tax to have fair distributional implications
Remind me: how does a spending tax disproportionately affect the poor? The tax goes into a local/federal budget, where poor disproportionately benefit from it (compared to what they put in).
Also, the arguably biggest global challenge in the next decades is going to be to slow/reverse the adverse effects of the global warming, which WILL disproportionately affect the poor (which have less ability to adapt or move). So how is doing something about global waring really disproportionately affecting the poor on the long run?