First of all, it makes it easy for the wealthy to lock the poor (and the rich) into their locations on the income graphs. The systems the wealthy can set in place are an impediment to a meritocracy by ensuring the rich stay rich and the poor stay poor, whether that is through boarding schools and trust funds or the Drug War and a toothless minimum wage. If the resulting massive disparity in wages implies one thing, it's that our civilization is wasting a lot of untapped human productivity on the low end of the wealth graph.
Secondly, it creates social resentment, fragmentation, and stratification. These are just emotions and Sociology Major words, yes, but that doesn't mean they aren't real. If the people at the bottom of the ladder feel like they don't have the power to climb, a society can end very badly as its political process becomes more polarized and communities are segregated.
Finally, it creates large gaps not just in material wealth, but political. Whether you're a liberal or a conservative, you think either the Koch Brothers or George Soros are destroying America. Either way, it can be agreed that democracies are undermined by a few unelected individuals wielding huge amounts of power. Less income inequality means less political inequality.
Nothing you said is wrong, but it's unhelpful. It distracts from how important dealing with growing income inequality will be in the future by saying "The discourse... is frustrating to me, because it's not pedantically right." It might be necessary if sama was arguing against large wealth disparities in a post-poverty civilization, but that is not what we have. Like you said: Poverty is the problem. And while we have poverty, poverty and inequality are closely linked.