It seems human nature complicates things. Perception of fairness trumps reason frequently [1].

[1] https://en.wikipedia.org/wiki/Ultimatum_game

IT would be hard to fight absolute poverty if the income of the bottom section never grows. You could theoretically tax higher and put welfare(or basic income?) but in practice that hasn't worked out very well, for both political and economic reasons.

Also, even if you give everyone a basic living with for example, basic income, income inequality is still a problem, because to get a bit more of what you want you have to sell more of what you do. This unavoidable causes tension, because labor , value and price can get distorted.

But not also that, because if you were to see that income inequality is a problem on how the value is captured, not created, this means that people with skills and capacity to create a lot of value are not getting rewarded for it, which is detrimental for all the members of society, except those that get the direct benefit of the value capture.

Social tension is very bad for the stability that allows us to ensure that all have access to food and medicine.

If you fight inequality you also fight "absolute poverty", and in a way (increased working opportunities, better wages, larger economy) that's better, and more respectful, for the absolute poor than charity.

>Wouldn't it be more important to fight absolute poverty than inequality?

Well that too, but the tension comes directly from the inequality. e.g. Being hungry sucks, but it sucks more if you see fellow citizens live like kings.