Interesting article. It is a reframe for me, since working with a financial advisor, I am used to the government "discount" on giving being a positive thing that helps people give. However, when I came across this statement, the whole thing started to fall apart for me:
A $500 donation by the person in the 35 percent bracket costs the person less than the same donation to the same place by the person in the 10 percent bracket. Because the same social good is ostensibly produced in both cases, the differential treatment appears unjust. If anything, lower-income earners would seem to warrant the larger subsidy and incentive. 
 The upside-down phenomenon is not specific to the tax deduction for charitable donations, of course. Deductions in general overwhelmingly favor the wealthy. In 1999, 50
percent of all tax deductions were claimed by the wealthiest decile of earners.
Because rewarding the lower-income earners for giving when it is harder for them and de-incentivizing those who can more easily afford it would seem to lead to a grosser disparity! The rich, with less of a carrot on giving, would give less, aka keep more, while the poor/middle class, with more of a carrot on giving, would give more, aka keep less! Does
that logic make sense to you?
I am interested in how we can incentivize giving to social justice. And I get that the article is in opposition to the "Greater Good" argument that philanthropy saves capitalism and democracy. However, I think they should have stuck with the question of: "How do we incentivize giving specifically to social justice through tax law?" That seemed a stronger and more robust case to me.