In other words make rich people richer and poor people poorer?
How, exactly, would this make rich people richer and poor people poorer?

Printing new money like crazy and distribute it only amongst banks, i.e. what the FED and ECB are doing every day,
that's what makes the rich richer and the poor poorer.
Shifting to smaller Bitcoin units can more or less be considered to be effectively the same as printing new money, except now it's evenly distributed along all current owners of money, instead of just a few elite monopolists. HUGE difference.