I should have specified, i was talking about classical liberalism. Social liberals are center-left to left wing.

The way i see it, the barebones definition of right wing and left wing is that leftism supports minimization, or abolishment of hierarchy, and equality, both class and social. You don’t have to be 100% of all these points to be left wing, just a degree of it.

The right wing believes that hierarchies are natural, and inevitable, or even desirable. They believe inequality is natural, due to social differences. Most of them believe that authority is good (not exclusive to right wing politics, there are authoritarian leftist ideologies) with libertarians and ancaps being an exception.

Classical liberals believe in free market, and generally have negative views on social services, taxes, and such.

Social liberals believe in a mixed economy, and favour social services, and believe in social justice (also class equality, but not a huge talking point for them). I think this makes them center, and at most, center-left (See social democracy or the nordic model). What makes them different than socialists and communists is that they are not quite radical in comparison to them, socialists desire to minimize wealth inequality (and inequality in general. politically, socially, etc) as much as possible.

Another point that you brought up is private property. I think this is also a defining factor on why I think liberals tend to be more right leaning.

You can still believe in markets, and be far left. Socialism, is when the workers own the means of production. It’s a pretty barebones definition, which makes it possible to have free markets, AND socialism. See Mutualism, Market Socialism, and Titoism