I am very confused. The Wikipedia entry of liberalism states that this ideology is based on the concepts of liberty and equality. Yet, these are in many senses not fully compatible. Think of a tax on inheritance. It might aim to reduce intergenerational inequality, but it is clearly a constraint on liberty. Alternatively, liberty as in free market might lead to monopolies and concentration of wealth, thereby increasing equality.
The wikipedia entry also refers to common ideals pursued by liberals, like
freedom of speech, freedom of the press, freedom of religion, free markets, civil rights, democratic societies, secular governments, gender equality, and international cooperation.
Many groups from the left would define themselves as liberals in terms of moral values (marriage, secular society, freedom of speech, gender equality, etc), yet are critical to capitalism as in free markets and property rights. Conversely, many from the right declare themselves liberals from an economic perspective, without strong advocacy for more progressive rights. In fact, neoliberalism is perhaps an example of the latter.
My way around this dilemma is that the original concept of liberalism was indeed based on both liberty and equality, insofar as it was a response to an agriculturally-based society founded in absolutism and conservatism of the XVIII and XIX centuries. However, when (i) capitalism became dominant, and the new elite of industrialist emerged, in opposition to the aristocrat, land based elite, and (ii) socialism as in Marx emerged as an alternative, the two concepts of liberty and equality were, in broad terms, no longer compatible, in particular when contrasting moral and economic dimensions.
As such, ideologies that emerged and built upon this original concept of liberalism, became much more refined later on. Therefore, the concept of liberalism no longer discriminates between these ideologies precisely, thereby being a poor tool to denominate a group of ideas. Liberalism then became a "misnomer". Is this a fair analysis?
For example, Paul Krugman, a Nobel-prize winner economist from the US, calls himself a liberal, but he is a Democrat, supporter of government intervention in the economy. He is clearly not a "neoliberal". Then, in the end, all this is to me very confusing.