Well you are making progress in that you now see that income needed to pay for half of FICA isn't subject to FICA reducing the effective rate from your original assessment of 15.3 down to 14.13.
Why is it such a stretch to see the income tax deduction, that the income needed to pay half the FICA increases in value by having that income subject to neither FICA tax nor income tax?
Imagine a person who has rent (or some other non-deductable expense) that is equal to the dollar amount of FICA they pay. Now answer this, assuming every hour they work pays the same, does it take the same number of hours of work to pay for both FICA and the rent? If not what is the difference?
No you don't add in the employers 1/2 of FICA to compute an employed persons effective tax.
Well I did warn you that the ordinary person has a hard time with this concept! It would have been instructive for you to read the supplemental tables on the CBO link I sent you so you could understand a few concepts that are used when discussing taxes and "effective" tax rates. The employer's half is added because it is part of that person's comprehensive income, it doesn't exist without their work, their production and it is paid solely on their behalf. If it wasn't added to their income, their FICA tax rate would be 15.3% (using your method of calculating) and you already know this is not true.
From the footnotes:
Notes: Effective tax rates are calculated by dividing taxes by comprehensive household income.
Comprehensive household income equals pretax cash income plus income from other sources. Pretax cash income is the sum of wages, salaries, self-employment income, rents, taxable and nontaxable interest, dividends, realized capital gains, cash transfer payments, and retirement benefits plus taxes paid by businesses (corporate income taxes and the employer's share of Social Security, Medicare, and federal unemployment insurance payroll taxes) and employee contributions to 401(k) retirement plans. Other sources of income include all in-kind benefits (Medicare, Medicaid, employer-paid health insurance premiums, food stamps, school lunches and breakfasts, housing assistance, and energy assistance). Households with negative income are excluded from the lowest income category but are included in totals.
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