The opposite of liberal is socialistThe opposite of conservative is progressiveThe opposite of libertarian is authoritarian
These three axes are theoretically independent of each other.
I think some will find this counter-intuitive because these terms are typically mixed up. We call authoritarian groups "far-right" and we think of liberals as of "the left". But I've always found this confusing and the more I study the history of liberalism, the less it makes sense.
These are primarily economic terms. Liberals are for small government, free markets, and laterly for monetarism (using monetary policy to control inflation). Socialists are for state ownership on behalf of the people, regulated markets, and usually take full employment as their economic goal. The original liberals were against democracy because it threatened a tyranny of the majority (which we have in the case of Brexit).
Many people will be confused by the association of liberalism with the right-wing. But all the key right-wing economic policies came from the classical liberals (Hobbes, Locke, Smith, Mills, etc).
To be far-right in this view is to advocate for allowing markets to decide everything without interference. In this sense, neoliberals who see a role for state in the markets are less right wing than the classical liberals. Mind you the role of the state is strictly limited to managing the money supply to control inflation (monetarism) and preventing monopolies. The latter has not prevented most industries seeing a massive contraction in the number of players. Virtual any class of goods and services you might purchase is not controlled by 3 or 4 companies globally. 4 oil companies, 3 food manufacturers, and so on. And though they are not monopolies these very large and dominant conglomerates have the same effect of suppressing competition. They simply swallow up any competition.
Socialists mainly advocate state ownership of the provision of basic services such as housing, utilities, education, and healthcare. In the past this led to full employment but also to inefficiency.
There are two distinct approaches to welfare. One of the classical liberal arguments for how the state should help citizens is "give a man a fish and you feed him for a day, teach him to fish and he can feed himself for the rest of his life." Liberals want to help a person to help themselves. What welfare liberals imagined is everyone with a fishing rod catching fish to feed themselves. Socialists take the approach that if the strongest members of the society go fishing with a net, they can catch enough fish to feed everyone.
But actually happens under liberalism is that a businessman captures the market on nets, boats, and fish and sells fish to people at the highest price they can extract from the people. In the name of freedom they make everyone slaves to this system.
Now socialism sometimes works well as it did in Scandinavia where everyone paid very high levels of tax (60-90%), but the govt ensured everyone had a job, everyone received an excellent education, very good healthcare, and they had the highest standards of living anywhere in the world. In other places, socialism led to stagnation as the state control was bureaucratic and apathetic. In Scandinavia government was highly motivated to look after citizens, whereas in Britain, with it's much greater population and history of rigid class distinctions, the system bogged down and worked against the citizenry.
As far as the environment goes, liberals treat corporations as legal persons who have the right to engage in economic activity unhindered by excessive regulation. Laissez faire attitudes meant that pollution, greenhouse effects, and habitat loss were acceptable consequences of economic activity, even if they negatively impacted on the health and well-being of citizens. This reminds us that liberalism has always talked expansively, but acted to preserve the privileges and profits of the elite.
Conservatives are for the status quo. The aging members of the Soviet Politburo were conservatives of the left. Americans who oppose changes to gun laws on the basis of individual liberty are conservatives of the right.
Progressives want to change things. One of the most striking changes of our time was the transition from Hick's interpretations of Keynesian economic policies to those of Friedman and Hayek interpreted by Alan Greenspan. I call this "progressive", not because it led to progress or was a good change, but because it moved decisively away from the status quo.
The problem here is that the term "progressive" is usually associated with progress towards some ideal. With liberals the goal is always individual liberty (though of course companies have the rights of individuals in law). Indeed liberals argue that liberty is not something the government can grant, because liberty is our inalienable natural right. Government can only limit or deny liberty. Most liberals accept, following arguments first made by John Locke, that there are a narrow range of situations in which the government may limit the liberty of an individual and that is where an action or activity harms another citizen.
Just as there are few if any socialists in the USA, there are few if any conservatives in the UK. The Conservative Party of the UK was historically a party which resisted change being proposed by liberals (free markets) and radicals (democracy). But they were taken over by neoclassical liberalism in the 1970s and began a series of massive social and economic reforms, completely changing how the UK economy worked, negating the power of labour unions, and privatising government assets and enterprises (crippling the ability of the state to help citizens).
I think these terms are fairly clear. Although the UK follows liberal (right-wing) economic policies, these have been adopted by governments who insisted we have no choice. They also happen to resist evidence based policies in favour of the moral commitments of the leaders - typically a "we know best" approach. And this is authoritarian. At the extreme are leaders who dominate (or attempt to dominate) the process of governing, like Trump.
Beyond this are absolutist forms of government such as what we see in North Korea or Saudi Arabia. Libertarians of the right or left (anarchists) are resistant to anyone telling the what to do.
And at the other extreme are the people who don't think the government should tell anyone what to do. These are often people who are already in a position of privilege who see the liberty of other people as a threat to their own power. This has been a feature of the history of liberalism - classical liberals resisted democracy for example, working against the extension of voting rights at every step.
Many libertarians turn out to be socially conservative. They don't want anyone to tell them what to do but they're against the expansion of rights for other groups. So we see US libertarians against the extension of civil rights to transexuals for example. Fundamentalist Christians are anxious to assert their absolute rights to freedom of assembled, worship, and expression, but some of them will murder a doctor who performs an abortion because they insist their worldview is the only valid one. Any libertarian who is against pluralism should face some hard questions, though they seldom do.
This is where I've got to in trying to understand political terminology and the dynamics that it applies to. I'll be continuing to think about for a long time to come I suspect.
It does seem helpful to understand where these terms come from and how the usage has changed over time. It seems helpful to disentangle some of the terms that have begun to merge: like liberal and socialist or liberal and progressive, and all of these with "left-wing"; or conservative and right-wing.
If we can call things by the proper name then it will help us to understand our differences and similarities. For example, although I see many of the liberal attitudes as pernicious in practice (if not always in theory) I can appreciate that the concept of liberty is one that they championed. Liberty is certainly something to celebrate, but it would be nice to spread it around a little more in my view.
But also I think it will be essential in the fight against the climate and biodiversity crisis to frame it in the values of the people we are trying to persuade to help us. Where liberalism is the dominant ideology, as it is in most of Europe and America, it makes sense to frame the discussion in terms of liberty.
If someone poisons the air I breath and thereby shortens my life or causes me to suffer, then this can be frame in many ways. But one important way to talk about, given the values of the ruling elites, is as an infringement of my liberty. It is fundamental to liberalism that if the government has any role at all, it is to prevent other citizens from infringing on my liberty, especially in the form of harming me.
The opposite of socialist is liberal
The opposite of progressive is conservative
The opposite of authoritarian is libertarian