Postulate: I'm in charge of a group of 30 children*.
Johnny has thirty apples. The other children have one apple each. I take away fifteen of Johnny's apples. How many apples did I give Johnny?
(A) Fifteen, because that which is not taken is given.
(B) Fourteen, because he's entitled to one.
(C) You didn't give him anything, you idiot! You only took from him!
If you answered (C), you're clearly a heartless right-wing lunatic and probably an Objectivist. Report to the re-education camp immediately.
Now let's examine how this exercise works in the real world.
I take away fifteen of Johnny's apples on behalf of the collective. Johnny voluntarily gives me, personally, two of his remaining apples. I strongarm the other children into giving one apple each to Johnny to reward his civic-mindedness. I then divide the fifteen apples of the collective among the children, giving half an apple to each of the 29 now-appleless ones and keeping the remaining half-apple for myself in payment for my services.
Note that I didn't give Johnny anything in this scenario... never mind that he now has twelve more apples than he started with.
And that, children, is how tax farming works.
*A horrifying thought, yes.