Tell me where the injustice creeps in

Time Zero
Right now, the universities in my state are funded by tuition payments.

Time One
I want to fully fund all of the universities in my state from tax revenue. I want it to be that no student will pay any tuition. I figure out that imposing a 3% income surcharge tax on the state’s residents would more than cover the costs of doing this. So I do it.

Time Two
I discover that the people who go and complete the universities are disproportionately rich and have disproportionately rich futures (to the tune of $1.05 million additional income over the course of their lifetimes on average). Poor people aren’t going to these colleges even when free because it is hard to do well in school when you are poor, and hard to go to college when you haven’t done well in school. So I amend the income tax to exclude everyone who didn’t go to college from the tax. The disproportionately lower-income people who are not beneficiaries of these institutions (that, by massive margins, disproportionately serve middle and upper income people) will not pay the tax.

Some people appear to think that when we move from time one to time two — excluding the disproportionately lower-income non-beneficiaries from the income tax that fully funds free higher education — injustice is introduced. From my perspective, I see this move as creating a more egalitarian income distribution, which I tend to like. I don’t quite understand why that’s an unjust amendment to the income tax I impose at time one. Maybe someone could explain where the injustice is.