All analogies are nonsensical in that they purport to demonstrate a point by making all other variables equal. This one was desgined to make a point contrary to the one that was made that an across the board tax cut is a tax cut for the rich. It did its job in that respect.
Instead of taking issue with that point (which I gather you could not )you attacked the analogy on two fronts, both of which were straw man arguments because they were points that the analogy were not designed to address.
The first was because it didn't take into consideration that the original tax was a fair allocation of the tax burden. You failed to demonstrate that the higher taxed person benefited more from Gov't services than his proportionate share. You apparently believe that its self evident.
Your second objection was we are only looking at one tax and we should broaden it to all taxes. However you conviently want to only include the payroll tax while excluding the numerous other taxes and also exluding the benefits derived by the payor of that tax.
1. If the top group currently pays 40% of the income tax but makes 60% of the income, giving it 40% of the tax cut disproportionately and inappropriately benefits that group.
2. If the income tax is more progressive than other taxes that are not cut, the net effect of an across the board income tax cut disproportionately benefits the top group.
Determining whether or not a particular group pays more or less than it should is a complex evaluation that ultimately involves subjective value judgments. You apparently believe the top groups pay too much. I disagree.