When you stated...
"When the statistics show that there are more wealthy and poor and fewer in the middle, then it's fact, not dogma."
Excuse me, but that's what you said. I'd like to see the source for those statistics. I don't believe they're true but I'm willing to review your source.
As for "Note that the "old saw" that you quote does not specify that one is the cause and one is the effect.", that has been the implication by many, but perhaps not you.
As for "And anyway, I thought it was children that the poor got.", I honestly have no idea what you meant.