I'm not talking about general taxation, which you're mixing with this.
I'm specifically questioning why one institution of "progressiveness" is right and another is wrong, when both are neither egalitarian in design, nor result.
As others have pointed out, when you transfer grades to lower performers, you are depriving them of a true education.
Can not the same thing be said, when you transfer money or services to a person, that are not based on educating them?
I'm not mixing up anything. Economies are driven by production and consumption of goods and services. In societies where poverty snowballs to encompass a substantial portion of the population, the production and consumption of goods and services slows down (because too much of the population's energy potential is inefficient), and unfortunately, it is exponentially easier to pass into the poverty threshold than to rise out of it -- you have to devote more resources to lifting people out of poverty than keeping them out of it. Since welfare keeps up consumption and production to higher levels than would be the case in a laissez faire society, more wealth is generated overall for all levels of society
over long periods of time.
Granted, when a person is a recipient of welfare, their energy potential isn't being utilized effectively, but welfare preserves them until such a point they can again become useful to the economy.
Consider: a person with a household and appliances has to produce or service a lot in order to maintain that household and appliances, meaning their energy is being directed toward actions that maintain civilization. If a person loses their ability to maintain that household during a recession and becomes homeless, then they lose most of their incentive and ability to keep applying their energy to useful ends, which both delays recovery and prevents economic booms from occurring once the recession ends. It's more beneficial overall to preserve households than let them slip into poverty.
That's one reason why welfare exists. History selected it for survival because civilizations that possessed welfare became stronger than those that did not. Welfare, for example, was an important institution in both classical Athens and Ancient Rome.
The ethics of this is that since a population that is actively maintaining households and appliances provides greater opportunity for profit than a poverty-stricken mass, high earners have a vested interest in operating a welfare system.
The same isn't true of students in a classroom. High-performing students have no vested interest in low performers (unless they have an arrangement with low performers in a curve system so that they don't have to work very hard for their good grades) and their lack of productive activity, because a classroom is an artificial environment where mutual dependence is far lower than in society as a whole.