Comment by epolanski
Economists argue that they are the fairest because they tax consumption rather than production.
Also everybody pays them, including people that avoid taxes (including criminal activities and tax evaders).
The argument against this is that lower income households pay more of it as a portion of their income thus the consensus is that to be fairest you need rebates and no taxes on many essentials (which is why often medicines or milk, bread etc have very low or no sales tax/rebates).
I think you're confusing fair with efficient.
IIRC, consumption taxes are more efficient in that, ceteris paribus, they result in the least economic distortion in terms of global wealth and productivity compared to alternatives like income taxes. But they're the least fair in the sense that those lower on the income bracket bear a higher burden in terms of marginal cost due to the higher fraction of necessary living expenses relative to income. Your first $1 of income and consumption has more marginal value to you and society then the second $1; so an X% tax on that first dollar has a higher marginal cost than X% on the second dollar. It's unfair in a very meaningful sense, not just a hand-wavy rhetorical sense; everything in economics is about marginal pricing.
Think of it this way, which has more marginal value, a) $1 spent on food required for a person to live, or b) $1 spent on a fancy fixture for a new yacht? The answer is (a), both from the perspective of the individual and society has a whole; society because $1 spent sustaining a living individual contributes more productive capacity to society than $1 spent toward a yacht fixture, even after accounting for the fact someone was paid to make the fixture.
AFAIU, it follows that efficiency and fairness (in the sense of marginal cost) are fundamentally related. But it gets really complicated from there--complexity that the "ceteris paribus" above is hiding--and drawing concrete policy conclusions much more fraught. Relatedly, consumption taxes can be structured in a progressive manner similar to income taxes, but... it's complicated; it's not so easy to ameliorate the unfairness issue, and once you start graduating rates it becomes difficult to compare schemes directly. For instance, I think just as a practical administrative and accounting matter progressive income taxation is easier to accomplish than progressive consumption taxation.