It is. And it's wrong. But part of how we got here is it was sold as not being a tax, even though it absolutely is.
The claim was it was a mandatory retirement investment program. Because the wealthy have their own retirements figured out they don't need their payouts to continue to scale with their income, so their payments in shouldn't scale proportionally either, under this flawed premise, since it is "not a tax."
But why it is a tax is, one, most of us will never see a payout because the program is going to collapse before most of us retire, and therefore it is NOT a mandatory retirement program. And second, all payments in and out of government are fungible, so it really is a tax and a separate retirement supplemental program, where we use language around them to pretend they are one program.
Ironically, if we took all the money that was paid into Social Security and invested it in a real portfolio (actual investment), our generation would actually get something, and current generations would be getting significantly more retirement. The issue is that because whether you like government or not, it is a money loser. It's basically designed to be one. That means using the government as an investment vehicle is in pure investment terms really really bad. Plus it also sets up a regressive tax as you pointed out.