It has to start somewhere. Start small. That’s what it’s all about.
Giving a bottle of water to the homeless guy is charity. It's the right thing for anyone to do, especially a Christian, but it's not his right to be given the bottle.
Fairness means, to my mind, that people should be reimbursed by society in rough proportion to their contribution to that society. I am, BTW, fully aware of the difficulties, both moral and practical, of deciding what a given person's contribution really is and in distributing it. But I suspect few people would argue that some people in our society are massively over-compensated for their contribution and other equally under-compensated. Though they'd probably often differ about who belongs in those two groups.
Redistribution, OTOH, is Marx, and others before him, all over. It uses the other definition of fairness, that of equal shares regardless of contribution. "From each according to his ability, to each according to his needs." Not as charity, but as the needy person's right. Which means, of course, that "stuff" must be taken from those with abilities in order to redistribute it to those with needs, by force if necessary. Which it always is, in the long run.
Was reading the other day about the Navajo, and their admirable tradition of helping their families. If a Navajo becomes successful, the less prosperous members of his family will show up, and he is under obligation culturally to share his wealth with them.
Of course, this eats into his capital, and therefore limits his ability to become even more prosperous. If he does so anyway, more distant relatives will appear and he'll have to share with them. But the author at the same time decried the relative poverty of Navajos as a whole. Apparently oblivious to the fact that the very customs she was lauding were a, perhaps the, main cause of that poverty.
If a Navajo man works harder and makes more money, he doesn't get to keep most of it. Has to share it with his less-prosperous relatives. So he has less incentive to work harder, and so do they. Spread that out over an entire society, and there will be a lot less work done and a lot less wealth produced.
In effect, you can have a lovely sharing society, but it will by definition be pretty poor. Or you can have a wealthy society, but it will be by comparison with others selfish and somewhat cruel.
What you can't have is a wealthy society that is kinder, gentler and more sharing. Pick one.