Treating someone differently because they have a lower income than others is discriminatory.Wealth is not a protected class; unlike gender, race, and religion, we don't have a legal mandate to avoid making decisions based on a person's wealth.
It's about everyone paying their fair share.
What does 'fair' mean, though? Another 'fair' scheme might be that everyone pays the same raw amount (rather than a fixed proportion of their income). After all, isn't it discriminatory to include a person's income in the formula for how much one should pay? Our tax code then looks like:
Tax(person) = requiredRevenue / nPopulation
Unfortunately, this ends up requiring poor people to pay more than they actually generate, requiring government to throw the poor in jail for tax evasion and tax more to cover the cost of the prisons.
Ok, so we should be allowed to use a person's income as a parameter to the tax equation. The 'flat' tax scheme is to use a formula like:
Tax(person) = fixedRatio x person.Income
The fixed ratio can again be figured out by looking at total income of the population and the required revenue.
Two major criticisms (amongst many):
a) The marginal utility of money is greatly increased when you don't have much of it. A 15% tax on $20k a year will lead to eviction, hunger and health problems, creating social ills that we'll need government programs to deal with. Or they'll just not pay the tax, so again with the prisons. And again, the overall tax needs to be increased to deal with a stupid choice in the tax code. This is inefficient and arguably unfair.
b) Furthermore, if we don't want to punish the poor for being poor, we have to reduce the ratio, meaning we greatly reduce investment in infrastructure, education, etc, mainly as a result of undertaxing the wealthy to avoid punishing the poor. This also seems hella backwards.
So maybe we end up with something like:
Tax(person) = min(0, r_0 + r_1 person.Income + r_2 (person.Income - baseIncome)^2)
with r_i fixed coefficients. So now we have four parameters to choose (or more, if we want a more general polynomial). And suddenly this requires real policy decisions to be made with some nuance...
So to me, it comes down to a question of whether we want to over-simplify the question of how to fund government - negatively impacting either a broad class of the population or drastically degrading the services provided by government - or whether we trust a segment of the civil service to do something a bit more nuanced.
I come down on the 'fix the fucking government' side, personally.