You said "A better comparison would be 30-years-olds of today versus 30-year-olds (whether the 30-year-old has or goes on to have children or not) of the past."

This is exactly what they did and what the data shows. 50% of kids today make more than their parents, vs 90% of kids 60 years ago made more than their parents.

I feel like we're missing each other points though...

Do see any material difference between these next 2 statements?

"50% of people today make more than their parents"

"50% of people today make more than people a generation ago made."

If yes, do you see how the difference might be relevant to whether people today have it easier or harder than people in the previous generation?

1) You have a fine point that it doesn't make sense to compare the percentage of (people who might have children + people who might not have children) to (30-year-olds of a previous era who went on to have children). In isolation, an absolute number like "50%" only has meaning if we assume that there are no significant differences in earnings between parents and non-parents.

2) Others are pointing out that the message of the graph is not the absolute percentage, but the trend line. The graph purports to show that the chance of greater earnings of (30-year-old maybe parents) vs (their own definitely parents at age 30) has decreased relatively linearly from 90% to 50% over the last 50 years. This could be explained by a demographic change in who has children over the same time frame, but it's not absurd to assume that the dynamics have remained constant even though the differences between the groups are unknown.

3) I'd be wondering more about how they accounted for inflation, since the manner in which this is done would drastically effect the results. I think the question essentially boils down to "at a given decile of earnings, does the average person today have a better life than the average person 30 years ago?" I don't know how one could answer this rigorously.

Do you see any worth in noting these two statements?

"50% of people today make more than their parents."

"90% of people 60 years ago made more than their parents."

If yes, what is the problem that you have with this study again?

It doesn't account for obvious confounding factors to prove it's conclusions of stagflation. Comparing parents to children has a pile of variables during this time frame that the article doesn't examine in the slightest.

For example it doesn't mention birth control once.

Everyone as a parent, but not everyone has a child. In both instances they are comparing "parents" a subset of the population. To "people" the total population.

Economic pressures can affect the decision to have children. Especially once birth control became widespread.