Classical liberalism arose in an era in which kings ruled and everyone else simply obeyed. Rulers and royalty believed that they had a divine right to make all the decisions within a society, and everyone else was resigned to curry favor in order to extract what little bit of self-governance they could squeeze out of the king. As philosophy and economics developed, it became obvious to the learned that leaving people alone to pursue their best sense of wellbeing just so happened to make any kingdom more prosperous. Eventually, the rulers of Western Europe realized that leaving their subjects to the greatest level of freedom possible also happened to produce the best and most prosperous outcome for the rulers themselves. We all know this story relatively well.
We could also tell a story about the same set of events using the lens of "fairness." In a world in which the subjugated are idiots and only the royals know what's best for society, the fairest outcome is that in which the rulers make the best and most reasonable proclamations. As subjects become more educated and less idiotic, fairness demands that they also enjoy some participation in the decisions of a nation. As the education and capability gap - and indeed even the wealth gap - between ruler and ruled becomes even smaller, then fairness demands that all people face more or less the same laws as all other people. Hence the end of monarchy and the rise of egalitarian democracy. Liberalism isn't only more prosperous, it's also fairer.
So, some of us have to worry about money a lot, while others of us do not have to worry much about money. Part of this comes down to different life choices; for example, someone who becomes a school teacher will never make as much as someone who becomes a heart surgeon. In a fair world, we're allowed to pursue different life choices as long as we are willing to live with the consequences of those choices. But another part of our wealth differences comes down to heredity. Some of us inherit an awful lot of wealth, and thus begin their lives with more prosperity than working class people will perhaps ever be able to earn, even if they make nothing but good choices for a hundred years straight. This inequality over the luck of being born doesn't seem fair to most of us.
When that unfairness is coupled with great financial hardship - such as crushing medical debt or the inability to afford decent housing - it's natural for some people to consider the merits of wealth redistribution. Perhaps taxing the very wealthy for the benefit of the very poor could alleviate more suffering than it causes. If so, society can gain, both in terms of fairness and in terms of prosperity. If it were possible, it would be a win-win: the poor would have much of their suffering alleviated while it would cost the wealthy comparatively little, and yet poor and wealthy alike would stand to gain from the benefits of a more egalitarian society, and perhaps a more prosperous one.
In the abstract, that all seems right. In the real world, however, we already live under a well-established regime of progressive taxation and wealth redistribution. This is true in every country I am aware of. Despite that fact, in every country I am aware of, there exists some debate about whether "the rich" should pay even more taxes and whether "the poor" should receive even more redistribution. The best answers to these debates, in my opinion, appear to be empirical. That is, we can analyze with reasonable accuracy the impact of variously imposed tax rates on economic behavior and determine relatively robustly which tax and redistribution rates are better, compared to others.
None of those economic analyses, however, can address the question of fairness.
For about a hundred years, libertarians and their precursors have been alone in the opinion that the wealthy should have some say as to the fairness of any wealth redistribution proposal. Most moral analyses will tell you that it's only morally fair to give money to a beggar who asks; it is only libertarianism that is willing to consider whether it might be immoral of the beggar to ask in the first place. It is most certainly only right-leaning strands of libertarianism that would suggest that the person being begged-from has a moral right to refuse.
This moral right to refuse is something that gives libertarians a bad name. We're often thought to be heartless and cruel because we believe that it's not fair to demand that the wealthy pay literally any tax rate approved through a democratic process. It's not that libertarians think that the poor should suffer, of course, it's just that many of us don't think it's fair to subject the rich to literally any tax rate, no matter how high.
Even some libertarians are uncomfortable phrasing it that way. Many would prefer to talk about the deleterious effects of high tax rates on the economy, or the non-existent benefits and ill effects on the labor market of wealth redistribution. They would much rather say that wealth redistribution is harmful rather than simply unfair.
The cynical explanation would be that libertarians are greedy knaves who want to keep all their money for themselves. This explanation fails mainly because few libertarians are millionaires, and the vast majority of millionaires are non-libertarians. There is something about libertarians that makes us keen to defend the rights of those whose tax burden is steepest on grounds of fairness.