here is the long explanation
1) the 50% taxable income was introduced in 1983 as part of the "bailout" of social security that Congress and Reagon agreed to. it's the same law that moved Full Retirement Age from 65 to 67 that Baby Boomers are now experiencing.
2) in 1993, it was raised to 85% taxable. the broad thinking is that similar to a pension, you contribute after tax money but the monthly payout is a function of that after tax payment AND the interest that has been credited over time. Congress landed on the 85% to reflect what had not been taxed to you previously.
3) originally, it was believed only 10% of the recipients would pay any tax - based on the $25,000 / $32,000 adjustments in the math. However, these numbers have never been adjusted for inflation and I suspect a lot more than 10% of the recipients are subject to their social security payments being taxable income.
https://www.ssa.gov/history/taxationofbenefits.html
