It's confuses people because there are different types of liberalism. Economic liberalism is right wing, social liberalism is typically left wing.
Anyone who has done any reading will be aware that liberal is a fairly generic term that has more than one meaning.
I would also advise anyone who believed that Adam Smith was right wing to do some reading as such a view displays a rudimentary ignorance as to what right wing means. While the term was not around while Smith was writing, his ideas flew in the face of a lot of conservative thought at the time.
Also, people using liberal as a synonym for socialist and then proceeding to think that liberals are socialists.
The term has been contaminated in the English language and this linguistic disease is spreading to other countries. Originally, the fault was in the USA, then also the UK: “As a supreme if unintended compliment, the enemies of the system of private enterprise have thought it wise to appropriate its label” (Schumpeter).
The way I personally intend it, liberalism is about liberty. It is the idea that the freedom of the individual (that is political, social and economical) is the most important value. In particular, liberalism needs political equality, while socialism is about socio-economic equality and is the belief that equality, in general, is more important than liberty. A bit simplistic, but in practice it proves an effective framework.
It is also interesting to note how Italian distinguishes political liberalism (liberalismo) and economic liberalism (liberismo). The two usually go together, but it helps, in my opinion, to attribute full dignity to the lofty doctrine of political Liberty, which we might even root back to Cato Uticensis and others, and economic theories which instead can be found wrong and only partially regard ideals, given that economics is half science half politics.
American political lexicon has changed the meanings of a lot of terms, "liberalism" and "libertarianism" among them; that doesn't make the American meanings of the words any less valid. They just happen to interpret the words differently, which is bound to happen in language.
"Classical liberal" is also quite a limited definition of pro-market liberalism. Ordoliberals are not classical liberals, and nor are centrists who also identify with the term "liberal" in several countries (the UK and Switzerland for example).
Adam Smith was not left-wing? I'd check that if I were you. The left-right spectrum is relative to different time periods, and in the 1700s Adam Smith was definitely left-wing. The right supported protectionism.
Also please stop confusing anti Globalist with 'far right'.
All the left wing parties in Britain self describe as 'liberal' as a euphemism for Globalist, but they are all for multinationals, the EU , open borders and free markets dictating the movement of people.
And they are anything but 'liberal' being against free speech and intolerant of those who disagree with them.
Liberal is anything those cuunts Cleggers, Davey, Faron and Cable like.