The starting point is the idea that the highest good is a freedom to be self-made. Right-liberals take this in one logical direction: they argue that if we are to be self-made then we should be self-reliant rather than dependent on the state.
Left-liberals take the same path as the liberal right for quite some distance. They too believe that the highest good is a freedom to be self-made. What does it mean to be self-made? Most mainstream left-liberals believe that we have made it when we succeed in the public sphere, for instance through academic and career success and the status, money and power that comes with this.
This view of what it means to be self-made overlaps with that of the liberal right. The liberal right believes that we become self-made through the market; the liberal left agrees that career success is a major part of "making it".
What are the impediments to being self-made? Possible impediments include those things that we don't make for ourselves, such as our race or our sex . For right-liberals, people who believe that such things matter in a public setting are "bigots" who are "prejudiced". In comparison those who are "enlightened" will be blind or impartial to race or sex in a public setting.
And here begins the divergence. The liberal left does not believe that relying on "morally enlightened" individuals acting through the market and within the institutions of a civil society will remove impediments to people being self-made. The liberal left believes that this will continue to allow impediments such as race and sex to matter, i.e. that there will continue to be inequality and therefore social injustice.
The argument of the liberal left is that society was created to privilege some groups (i.e. white males) at the expense of others. So the problem is a systemic one rather than a matter of individual bigotry or prejudice. It doesn't matter if a white male is an enlightened progressive, he still occupies a privileged place within the system. It is whiteness and patriarchy, and a systemic racism and sexism, which have to be overcome through a radical, if gradual, transformation of society.
And what are the agencies for such a transformation? First and foremost the state. Second, social movements of the oppressed, such as women or minority groups.
Which brings us to a series of contrasts between left and right liberalism, despite the similar starting point.
i) The right has a more positive view of civil society. Right liberals don't want individuals to be dependent on the state. So they look instead to a social structure built around civil society (but the emphasis is usually on voluntary associations rather than natural ones). In contrast, the left is more likely to see the institutions of civil society as being manifestations of the patriarchal or racist system designed to privilege some over others. For the left, the ideal is more commonly the individual being guarded in his rights, and supported in his lifestyle choices, by the liberal state.
So the contrast is "individual & civil society" versus "individual & state".
ii) The right is more likely to think that society can be best regulated by the actions of a free market. Millions of individuals will compete in the market and the result will be to the larger benefit and progress of society. The left though has tended to see this as producing an unacceptable level of inequality and has looked instead to the neutral expertise of a state bureaucracy to regulate society. In 1928, the English Fabian Beatrice Webb explained this preference as follows:
What bound us together was our common faith in a deliberately organised society – our belief in the application of science to human relations, with a view of betterment...we held by the common people, served by an elite of unassuming experts
The contrast here is "society regulated primarily by the market" versus "society regulated primarily by state experts".
iii) The right has focused to a greater extent on equality of opportunity, the left on equality of outcome. This has come up in the news recently, with claims that the Democratic administration of Barack Obama is going to sue companies or schools for race bias, even if the rules of those institutions are applied equally to the races. If the rules are thought to have "disparate impact" (a greater effect on some races than others) then the charge of racism will still apply. This might include, for instance, a bank which has certain lending rules, which leads to some races getting loans at a higher rate than others:
Under this broad interpretation of civil-rights law, virtually any organization can be held liable for race bias if it maintains a policy that negatively impacts one racial group more than another — even if it has no racist motive and applies the policy evenly across all groups.
iv) The right wants the public actions of individuals to be colour blind, i.e. people are not to act as members of "tribes" or "collectives" (but a private, sentimental attachment to an identity is more acceptable). But the left wants people to actively see race or sex so that institutional privilege isn't hidden and is confronted. Furthermore, the left views public, organised, political action by women or minorities as liberation movements which can be harnessed to deconstruct white male domination of society and so the left is more open to identity politics. Also, given that the left locates racism within whiteness, this then means that other traditions get a pass and can be viewed more favourably as colourful expressions of culture rather than as means of domination and oppression.
So the contrast is that the right is more hostile to the role of collectives or tribalism in the public sphere, whereas the left runs with a kind of identity politics.
All of the above forms the ordinary political discourse of Western countries. It can be difficult to see a way through it, as politics is framed so tightly around it. Many people react by getting defensive ("I'm not sexist") or they join the political drift in which those who want to be supported as individuals by the state and those who believe that the left identifies with them as women or ethnic minorities go for the left-liberal party, whereas those who see themselves as part of a stable family unit or who believe that they are targeted by the left-liberal party as men or as whites go for the right-liberal party.
But that leaves things as is. The challenge is to move beyond the confines of a liberal politics, whether of the left or right variety.