why should I subsidies whatever you want to have
  happen beyond that point?

The theory is tax breaks for charity make people donate more, and a dollar donated to a charity is a dollar that doesn't have to be paid by the government to do the same thing.

For example, if I donate $1000 to a university, higher education is $1000 better funded. Whereas if the government taxes me $330 and gives that to the university, then I spend the rest of the money on hookers and cocaine, higher education is only $330 better funded.

If you're a conservative, you might also think the government is inefficient and most of that $330 would be wasted in the bureaucracy; that most donors are basically like you and hold your views because charity is a christian virtue; or that donations allow donors to choose efficient charities in a competitive market, driving down waste. If you're a liberal, you might think most of that $330 will be spent on costly foreign wars and private prisons; that most donors are basically like you and hold your views because charity is about putting the good of that many above yourself; or that donations are key to supporting causes like animal welfare and vegetarianism that are unlikely to get state funding.

Needless to say, the above assumes charities are basically moving towards the same public good the government is trying to achieve. If I donate to support schools with extremist religious views or to support the families of Palestinian suicide bombers, that's a different matter.

Edit: And complete alignment of charities with the views of government isn't required. If the tax deduction turns $330 into $1000, the charity only needs to be 34% aligned with the government for the outcome to be better; so for example $1000 donated to a religious school that spends $500 on textbooks and $500 on bibles is better than the government giving $330 of textbooks.

I agree, if this is the rationale for charity tax deductions, that there should be strict auditing for sham charities and charities that are wildly out of alignment with the public good.

> The theory is tax breaks for charity make people donate more, and a dollar donated to a charity is a dollar that doesn't have to be paid by the government to do the same thing.

The second half of this theory is obviously unsound when the definition of "charity" is not limited to functions that would otherwise be performed by the government and which directly reduce government expenditures in those domains.

It is especially ludicrous when the definition of charity for which subsidies are provided includes, e.g., religious institutions, which perform functions that the government is Constitutionally barred from performing, which are obviously not functions that the government would otherwise be required to perform.

(The first half -- that providing a public subsidy for an action encourages that action -- is true, but it doesn't make a lot of sense for that to be an income-weighted subsidy. Were the second half sound, the first half would be better served by a tax credit for, or proportional to, the amount of donations, rather than a tax deduction.)

Rather than the "same goods" argument, I would say that charitable tax deductions moves the agenda and decision-making process of what specific public goods we want away from the political process (i.e. the people voting in politicians who promise to fund/promote/ xyz) to private (read: wealthy) individuals, which is why I think conservatives favor it more. Conservatism views Oligarchy as a Good Thing.

When the public good is funded by the wealthy (through philanthropy) rather than by the government (through taxes), then only the wealthy get to decide what counts as "public good". At least I can (in theory) vote out the government. I can't vote power out of the pockets of the wealthy.

This assumes everything charities do the government would also do which is clearly false. Thus invalidating the argument as said by your last line.

So, I don't get the point? Is this one of those cognitive dissonance things where you are supposed to accept two things that can't both be true?

In your edit nothing suggests there is even 10% alignment on net. Remember, many charities have negative alignment by acting counter to the governments intent.

Even in areas where it looks like things align say non religious textbooks failing to teach evolution has very real and very negative results, just look at antibiotic resistance. The long term impacts of that may very well outweigh all positive effects of charitable giving in the US.

And it's not just education. Handing out AIDS medications in poor counties sounds great! Doing so poorly may quickly make those same medications useless.