A big part of the problem is that the terminology – “inequality” – is terrible.
Literally no one, including the most strident leftist, believes that everyone, from the brain surgeon to the floor sweeper to the unemployed person unwilling to work should receive the same exact income and possess the same exact wealth. A much better term would be “increasing concentration” rather than increasing inequality. Framing the problem as an increasing concentration of wealth and income would resonate much better with the American public and do a much better job of conveying the intended idea.