From a purely financial, self-interested standpoint, how does a donation to charity which reduces taxable income actually help a person? If I reduce my income by $100, it's true I won't have to give the fraction of that to the government that I might have, but now rather than being out a fraction to the government, I'm out the entirety to the charity.

Even in the case where the donation drop the payer to a lower tax bracket, I don't see how it helps. Any insight greatly appreciated.