> If you give $1000 to a charity, the tax deduction doesn't affect that.

If your marginal rate of taxation on income is, say, 35%, then you give up only $650 in disposable income to donate $1,000 to charity. Without the deduction, someone in that circumstance who could afford to give $1,000 with the deduction could only give $650.

Or, looked at a different way, someone with that tax rate who "gives $1,000" to charity is really giving $650, and the government is giving $350.

Well, my point is that the charity still gets $1000 regardless of tax rate. You could increase how much you give based on your expected tax savings so it costs you $1000 after the tax refund, but it's not automatic.