In order to improve global health or address other issues that impact countries beyond where you live, the government (even an idealized version without waste, corruption, or political games) might not be the most effective way to accomplish this.
What I find kind of interesting is that Bill Gates and Warren Buffet argue that they should be taxed more, but they don't do anything to further that goal aside from media soundbites and headlines. They could fund an incredible war chest for a lobbying apparatus who's sole purpose would be to create a more fair tax system. But no such thing happens.
It seems fortunate that some charitable funds isn't subject to that risk. There are other risks, but they seem lower.
In an imperfect world, government funding alone seems insufficiency diversified. That's too much power in one place.
This is only ever true if you assume that government tax spending is 100% efficient, with nary a fraction of a cent being wasted. I don't think that's a safe assumption.
You lowering your tax rate and giving that money to charity isn't magicking more money into the world, it is just a different allocation.
The government's tax income is allocated by the masses (in theory anyway). It is fair and dispassionate.
Philanthropy / charity is picking winners and losers based on your personal whims, and for many it is about gaining social capital.