Long story short TC says that if you assume that the rich have an unfair advantage because they can use their wealth to make more wealth then it makes sense to redistribute from the poor to the rich.
Well, if you give a rich guy $1000 then he is going to use his superior connections, education, prior wealth, and other unfair advantages to grow that $1000 into $10,0000 or eventually $100,000.
If you give it to the poor guy then basically the poor guy just has an extra thousand.
Even if you believe the trickle effect is very small, say 2%, then the poor guy is still better off when the rich get a $1000 than when he gets the grand. After all, eventually the rich will have $100,000 and if even 2% trickles down then that $2000 for the poor guy.
Whats the problem with this story?
Well, TCs logic rests on the fact that the returns to more money are constant for each group, however, the redistributionist believes that they are not constant at all.
In fact, the redistributionist is implicitly assuming that the returns to money are S-shaped and that this S creates a poverty trap. What the poor need is a Big Push to set them on the road to wealth.
On the accompanying graph one has to get beyond $100K or so in wealth before you can really enjoy the returns the rich do. The goal is to get everyone beyond the $100K point.
Now, I'm not arguing that the S-Shaped poverty trap theory is true but it is the logic behind redistribution.
Note: The point here isn't that $100K specifically is a special value. Its that there is some level which changes the game. If the poor are given some level of redistribution then new options are opened to them. That level could $100K it could be $30K.