Let's start with what is not wrong with the welfare state.
Much criticism of the welfare state focuses on how it encourages dependence not only on the government, but dependence on others per se. In some circles the wish for a social safety net is disparaged as a moral flaw encouraged by people who want to subvert humanity in general and the original liberal, or libertarian, project in particular. The welfare state is said to clash with such alleged and desirable virtues as rugged individualism and radical self-reliance. In this view the welfare state robs human beings of their essential character as independent persons--that it corrupts them with handouts and makes them parasites on the labor of others. (Such corruption of character cannot be ruled out as a consequence and can be found in some degree in the United States, but it is not inevitable because culture surely plays a role in how people respond to political incentives. See the case of Sweden and other countries in Scandinavia, which combine a "generous" welfare benefits with a substantially free-enterprise system.)
You ought to be able to spot the problem in the first step of this criticism of the welfare state. In the original liberal project, rugged individualism and radical self-reliance were not guiding principles because it was understood that people have always lived socially. The first liberal theorists knew this and had no wish to change society or human nature in that respect. In other words, people were always interdependent and dealt with one another in continuous mutually advantageous ways. That's what society is. A human being living in isolation is not fully human.
Of course the ways of social living changed over time. For example, circles of trust grew, transcending family ties, and the division of labor expanded as technology and political institutions permitted. Dealing with strangers, once unthinkable and highly risky, became increasingly common as people glimpsed the gains from trade and other benefits of social contact. The ideal was to live interdependently to mutual advantage with others. Thinkers like Frederic Bastiat in the 19th century understood that well.
What's the appeal of social living? The question really doesn't need answering because the truth has been so obvious since antiquity. Peacefully interacting with others as a way of life magnifies our individual intellectual power, our ability to produce, and out emotional satisfaction. For example, as a practical matter, an individual may know something about a subject, but that person surely won't know everything about it. Much is to be learned, then, simply by talking to other people, not to mention reading what others have written. A person is likely to learn more about a subject even when talking to an ignorant but inquisitive counterpart because just answering questions can lead to an extension of one's knowledge though the emergence of overlooked connections. John Stuart Mill had this sort of thing in mind when he wrote in On Liberty, "He who knows only his own side of the case knows little of that."
Society extends our intelligence. But that's just one of the many benefits of social living.
Aristotle makes the point that continuous peaceful interaction with other people is the rational mind in action. As reasoning animals, we need that to live according our essential nature. Justice, respecting people's rights, that is, the commitment to interaction via reason, fosters the flourishing of everyone concerned.
An obvious fact bearing on this subject is that social life takes place in a world of uncertainty. No one can know what personal and social misfortune lies ahead. Therefore everyone has an interest in hedging against calamity. Insurance, the pooling of risk with others, is an old institution, and no one would say that someone who buys insurance against bad luck is shirking his duty of self-reliance or seeking unreasonable dependence on others.
This point should sit well with any advocate of individual liberty and global free markets in which people, goods, and money moved around according to the preferences of the individuals involved.
Superficially, the welfare state can look like nothing more than than the formalization of this legitimate liberal (libertarian) social welfare principle. That could explain why most people accept the welfare state to some degree. Welfarism can appear to be a proper plan to address our entirely reasonable concern about the risks of an uncertain future. You pay in when things are going well; you draw out when they aren't. That's where libertarian analysis comes in. For the welfare state's appearance is misleading. Moreover, the state's underlying flaws point to a better way not toward fostering fictional atomistic individualism, but toward a moral and more effective way to address our rational need to hedge against an uncertain future.
Then what is wrong with the welfare state? The two biggest flaws stem from its nature as a government institution. The welfare state is coercive, and it is monopolistic and anti-market. As a tax-financed institution, the welfare state is obviously coercive. The fig leaf of democratic representation aside, taxes are compulsory payments. They are not like club dues or prices in a shop. As a taxpayer, you cannot say no.
It follows that a tax-financed arrangement has little in common with a market or noncommercial voluntarily financed service. If consumers are free to say no and buy elsewhere--as taxpayers are not--then service providers must be responsive to customers in a way that no government must be. Otherwise, they could go out of business. Moreover, free consumers provide critical feedback to providers, which tends to improve service.
On the other hand, a government system is subject to what are known as public-choice and (Austrian-school) knowledge problems. That is, first, the bureaucrats and politicians who run the system have their own personal agendas (like career advancement and power) that may have little to do with the good of the people they ostensibly serve, and second, even if their incentives were perfectly aligned, they couldn't know what they would need to know to do the best job possible because the competition and consumer feedback that freedom generates would be absent. Ludwig von Mises showed that without market-generated prices, economic calculation and hence efficiency in the use of scarce resources are impossible, and F. A. Hayek showed that crucial knowledge related to what would serve our well-being is scattered throughout society and much of it is never articulated. The only way to obtain that knowledge in a usable form is via the prices that emerge when people are free to express their preferences through market activity.
These are serious practical flaws. Because of incentive and knowledge problems, even a modest welfare system that at first addressed only actually unfortunate people may not stay that way. Political dynamics may tend to bring expansion far beyond the original mandate, leading to fiscal problems, slowed economic growth, and liberty violations. And because of knowledge problems, blunders could abound in the absence entrepreneurship to sniff out and correct error.
In contrast, since all participants in an unmolested competitive marketplace and the larger noncommercial voluntary sector are free, providers have to work to win consumers over, that is, to persuade them that their offerings are superior to those of competitors. Hence, they must innovate, exhibit entrepreneurship, and find ways to lower prices and enhance quality. It is no accident that the market, even a heavily regulated one such as ours, displays more imagination than governmental service providers. Competition makes it in people's interest to spot and correct errors.
These considerations lead us to conclude that what's wrong with the welfare state is not that it caters to people's concern with uncertainty, but that it does so in a coercive and inferior way to other alternatives that would be available if the government did not crowd them out. That's a damning indictment. (It has also been shown that the welfare has been politically intended to keep poorer people who have been exploited through crony capitalism from rocking the boat by giving them money and other benefits and so keeping them quiet.)
What are the alternatives? We can point to two broad categories: for-profit market institutions and what were once known as mutual-aid organizations. The first group would include commercial insurance firms of all kinds. The second are voluntary organizations that are cooperatively owned by their members. The largely unknown history of mutual aid offers excellent ideas on how people can grapple with uncertainty without the coercive state. (For details see David Beito's landmark work From Mutual Aid to the Welfare State: Fraternal Societies and Social Services, 1890-1967.)
In their heyday mutual-aid organizations, also known as lodges and friendly societies, were largely working-class associations that not only provided an arena for camaraderie but also elaborate methods of obtaining a variety of insurance benefits and even medical care, including hospital services. It was an extraordinary chapter in American (and British) history that holds the key to replacing the costly, debt-ridden, and ever-expanding U.S. welfare state with a free, innovative, and flexible arrangement capable of catering to a variety of needs in an uncertain world.
Who knows what services would be available today had mutual aid not been subverted by the welfare state?
TGIF--The Goal Is Freedom--appears on occasion Fridays. Topics discussed here are also addressed in my What Social Animals Owe to Each Other and Tethered Citizens: Time to Repeal the Welfare State.)