Sure, so adding poor people to a rich world and averaging out the resources is bad, not good, and we shouldn't do it.

Which step(s) do you disagree with? Adding poor people or averaging the utility?

Parfit defends the first step by saying that it's a "mere addition". Poor people on they're own are (somewhat) good. Rich people on their own are good. Therefore the combination of the two is better than either.

The second step (averaging the resources) is supposed to be intuitively obvious. We can tweak the mathematics so that the quality of life of the rich only goes down a tiny amount to bring the poor up to their level. If the rich could end all poverty by giving a very small amount wouldn't that be the right thing to do?