A lot of leftists (and I hardly ever saw it before coming on Lemmy) use 'Liberal' to mean Classic or Neo Liberal - basically a synonym of capitalist.. That's not at all what it means in American politics, where it means the opposite of Conservative. If we used that definition, Conservatives would be called Liberals as well as Liberals being Liberals, which obviously makes no sense for US lingo. However, they both are Liberals in the neo/classic sense as most US Liberals aren't calling for communism.

Liberalism isn’t necessarily a left wing ideology.

It's an inherently right wing ideology lol. They're just conservatives that want/like to think they're progressive.

Liberal economic theories beleive the free market is the best solution generally, but allow the free market to be intervened in or even entirely supplanted in cases of market failure or where significant social problems arise from private ownership. There is a lot of debate inside liberalism as to when a market has failed, or when a social issue requires intervention, which is why sometimes you will see centrist liberals and left liberals arguing. Just look at Canada with our Liberal Party, its a big tent party with a small social democrat rump(since most social Dems are NDP), a larger social liberal / left liberal group, as well as some centrist and "blue liberals" (these would be right liberals, who are harder to convince about market failures).

Liberalism can be progressive, especially when the main thrust of a liberal party is left liberal or social liberal. Some Liberal parties are progressive sometimes, then more centrist at others as members and the membership changes over the years (or often on the strength and leanings of their leader). All still liberalism.

That’s only true if you use the international definition of “liberal”. In America, “liberal” means “left wing”. And we’re talking about American politics.