First off, my money doesn't grant me power over anybody and it's still money. That leaves only one logically possible version of your statement and the correction looks like this: "A world where being rich doesn't grant power over others is one where big money isn't big money"
In that form, your statement is perfectly logical, if somewhat tautological, but there is another problem with it and it's a real huge one: No textbook has anything like that and no school teaches it either, even the media is vary shy of talking about it.
At a first glance, that's not your problem but it definitely has to be, meaning, you and the people who gold similar views, should become loud public proponents of Speaking Truth to the Powerless (tm).
We can no longer have this cognitive dissonance economics that teaches that money is means of exchange, unit of account, etc, but skips the most important truth: that big money is, first and foremost, a tool of power over small money.
Only after this educational task is complete, your explanation will have the right to exist and be heard.