I think that it means that I get to deduct it from my taxable income, just like my mortgage. It's a deduction (unless I'm subject to one of the various phaseouts or am better off with the standard deduction).
Do you think that people think that the $5k standard deduction reduces their taxes by $5k? (I forget the exact amount because I itemize.) If not, why do you think that they're confused by the phrase "tax deduction"?
There's a huge difference between a tax deduction and a tax credit. I suspect that most people who pay taxes understand it.
If you think there are legions of taxpayers who don't get this, you are mistaken.
Imagine that you meet a person who is terribly confused about logic and evidence to a point where he takes any random anecdote or even a lack of one and reinterpets it as data backing his preconceived notions. Now imagine trying to set this person straight and help them out of this trap. Do you think he would resist the change and take it as a personal affront? Well, there is always a slight chance that it will help.
