It is common, upon finding out that libertarians oppose coercive wealth redistribution, to accuse libertarians of opposing charity as a whole. This is due to a basic confusion between macroethics and microethics.
Macroethics is the ethics of the macro scale, much like macroeconomics. It encompasses two fields; politics and economics. Microethics is ethics on the personal scale, the more traditionally understood field of morality. Of course the distinction between the two is as artificial as the distinction between microeconomics and macroeconomics, but doing so is useful to understand how the macro and the micro are different, just as in economics.
The two fields do relate, as is to be expcted, and holding certain macroethical positions will necessitate holding certain microethical positions, and vice versa. It is impossible to consistently hold a political belief opposing the initiation of force without also holding the moral belief opposing the same.
But the connections aren't direct and easy to misinterpret, much like how the connections between microeconomics and macroeconomics are not direct and easy to misinterpret. One can point out how microeconomically it doesn't matter to an individual whether his wage comes from the government or from the private sector, as long as he is working he will have both the satisfaction of a job and the satisfaction of an income. It takes looking at the matter from both the micro and macro perspective to notice the essential difference.
And it takes looking at ethical activities from both a micro and macro perspective to correctly identify them. Accusing a libertarian of wanting people to starve (microethics) simply because he opposes wealth redistribution (macroethics) is an unwarranted extension. It is quite clear that the two positions are in the two different fields. Having identified that they are in different fields, one can then challenge the person claiming there is a connection to substantiate the claim.
Since the extension is unwarranted the claim cannot be substantiated. But a converse claim can be made. This converse claim will be a lot harder for the critic of libertarianism to defuse because it invokes the critics own logic. By claiming that force of government is needed because otherwise old people will be starving in the street, the person making the claim is admitting an unwillingness to care for family members if not forced to by the government. It is also a spurious claim.
The ability to distinguish between the macroethcial and the microethical, between the political and the moral, is important. The ability to point out the different is also important. It enables one to put away the fallacies that libertarians often face.