Quoted:

Cool, I'll try once more without the math since I see that it is confusing to you.

Concept 1:

Imagine you are in the Chick-fil-a drive through.  You go to receive your Spicy Chicken Sandwich and the person manning the drive through window tells you it has been paid for by the car in front of you.  You in turn pay for the car behind you, who in turn pays for the car behind them, ad infinitum.

Under this model, did you get a free sandwich, or did you pay for it?  I'll assume you're clever enough to realize it was not free, and there is functionally no difference between "paying it forward" and paying for something directly.  Under either scenario, you have one sandwich and you have $5 less.

Concept 2:

I assume you are familiar with The Ant and the Grasshopper by Aesop.

In the fable, the Grasshopper dies of hunger.  Our reality is that Grasshopper takes part of the Ant's food (via taxes and redistribution).  This means less for the Ant.

Now imagine that as the Grasshopper hops about, there was a mechanism to force the Grasshopper to save some food, not necessarily enough, but some.  That would mean he would eventually take less of the Ant's food than if that mechanism did not exist.

Conclusion

We acknowledge that "paying forward" is the same as paying for it.

We acknowledge that if we require the Grasshopper to pay for something, it ultimately means a bit more for the Ant (or rather that the Ant will eventually subsidize the Grasshopper less).

While it could be improved in many ways, this is fundamentally what social security is.

Whether it is a "tax" is irrelevant.