I might sound like a sucker, but that's just always been my thought on it. My mother once said something to me like that as a kid and I've applied it donating.
Also, notice that you're not somehow "getting something back" from other taxpayers in this scenario. You're just lowering your tax bill.
The historical reasons assume that many everyday community efforts (feeding the hungry, sheltering the homeless, abused women and children, planting trees, sheltering stray animals) is better done (and financed) at community level by community efforts rather than by central government and sending money to Washington D.C.
I don't understand how this is considered tax avoidance? It's not like you get more money this way, you just get to give slightly more to charity than you might otherwise, which is the point of the deduction.
With charitable giving you can avoid taxes but still retain exactly the same after-tax income (assuming that you were going to gift to charity regardless of whether you got deduction or not). That is, you can gift $100 to charity, deduct the gift, and so avoid (say) $30 in tax. In this case the gift to charity effectively results in you having $100 less than before. Or, for same net result to you (minus $100), you could gift (after-tax) dollars to charity, say $70, and pay the $30 in taxes that you avoided in previous scenario. Only in second case you ended up giving only $70 to charity, because $30 goes to government. In first case you gave all of the $100 outlay to charity, avoided the $30 tax.
The linked article seems to suggest that Zuckerberg is trying to take advantage of the system by gaining tax-exempt status while effectively _not_ making charitable gifts, that he is somehow trying to pass everything to the child while taking advantage of tax-exempt status of a charitable organization. I'm skeptical both that his intent is to try to do this, and that there is any scheme that could legally accomplish this.
On a different, but related, note, if I were a parent with $40Bn (or $30Bn, $20Bn, $10Bn, or even $1Bn) I would certainly avoid any plan where the bulk of my estate was to be left to my child. Having that much money is a big responsibility, and it's not something that's likely to add to a person's quality of life. Quite the contrary, it's likely a hindrance, not something I would want to saddle my child with. At most, leave them some large amount ($5M, $10M, $20M, $50M?), something basically guaranteed to make them a wealthy person who doesn't need to worry about money, but hopefully not enough to require that responsible management of their fortune be a main focus of their life. (I realize there are moral implications of having that much money for anyone who has even $10M -- perhaps even $1M -- but when the amounts get astronomical, say to hundreds of millions or more, the moral responsibility really does -- or should -- become almost overwhelming. Not a burden I'd want to put on my child.)