Your link is about rate of growth of population, your claim is about population.
The basis of your first paragraph will be true in the future, but is not yet (unless you define 30s and 40s as old).
The thing that makes the dynamic in your argument true is that young people do not (or cannot) vote and participate in the political process as much as old people can.
We have people who can no longer produce, but want to consume (and their potential beneficiaries) on one side, and on the other we have people can produce. The former group need to collect rent from the latter group, otherwise they offer nothing to the latter group in exchange for their production.
Which is funny when I see young people advocate for income taxes, when they should be advocating for property/inheritance taxes.
https://www.populationpyramid.net/united-states-of-america/
Those in their 30s right now are the biggest proportion.
And 20 or 30 years ago, that population pyramid was even more tilted towards people in their 0 to 30s (obviously).