Suppose you have N poor people (however you define the term) living in society. Suppose also that it has been decided that direct handouts are not good policy and the key to ending poverty is creating opportunities for the poor to raise themselves out of poverty through education and work programs.
Given the existence of free will--and, oftentimes, the preexisting habits or circumstances that led to being in poverty in the first place--equal opportunity will not create equal results. Some of the poor will take advantage of the opportunities given (call them group X), and others will not (group Y).
After some time T after implementing said social programs, let's suppose Group X has successfully used those given opportunities and are no longer impoverished. Group Y, by definition, has not, and remain poor even after the anti-poverty programs have been implemented.
This would seem to indicate that as long as Group Y (and free will) exists, poverty can NEVER be completely abolished. Even the most optimal social policy to end poverty will at most reduce N by X, since Y will remain in poverty regardless of the opportunities presented.
Here's the problem: how do we know this has not already happened? What if the quantity of people in poverty today are already just the Group Y people who remained after the Group X people left. I'm not suggesting this is the case, but if it was, how would we know? What if current policies were already the most optimal anti-poverty measures one could create? Could we prove otherwise?
Some people seem to say the existence of people in poverty shows that current social anti-poverty policies are inadequate. The inadequacy part is no doubt true, but the mere existence of poor people is not evidence of it. Since we can't tell by looking at someone whether they are Group X or Group Y (and people can change from one to the other through time as well...) how would we know if we already had the most optimal anti-poverty measures in place possible? How would we know if we had already done all we could?
How do you judge the success or failure of an anti-poverty measure, anyway? Raw numbers? Percentages? Either measure fails to take into account the difference between groups X and Y--if Group Y happens to be increasing for whatever reason, the ranks of the poor will increase percentage-wise even if you had the best anti-poverty program in the world in place already...
Important factors to consider in the debate about poverty and 'income inequality': what defines success or failure? How do you help Group Y people get out of poverty? (Or can you?) What metric can you use to determine if existing programs are already as successful as possible, or if change is needed? Without going through individuals case-by-case, how can you tell whether someone has already been given ample opportunity to escape poverty and thus current policies are adequate?