I demonstrated this with an example, where we know what caused a price change (supply chain issues for a substitute product plus increased demand) and know the distributional effect (higher margins for sellers of used cars). If we naively try to explain the price change based on the distributional effect, we would claim that higher prices were purely caused by increased greed. We know this to be false.
Look, perhaps companies really did become more greedy in 2020 and that's what has really caused inflation. Or maybe large amounts of stimulus caused increased demand. Or perhaps the war in Ukraine has caused supply chain issues which drives up prices. My point is that looking at the distributional effects of inflation is just completely disconnected from the question of what caused inflation in the first place.
At the very least, if you're claiming that we can figure out what caused inflation by looking at the distributional effects, can you provide some evidence, or some argument, to support that claim? Because I think my example demonstrates that common sense ("X benefitted from inflation, therefore X caused inflation") is not a good guide here, and if anything, the additional complexity of real markets works against you here - if we can't even explain inflation based on distributional effects in a toy market, what makes you so confident we can do so in the market as a whole?