Liberalism can be right wing or left wing.

Eh. Its traditionally in that "economically conservative, socially liberal" pocket, wherein you can do whatever you want so long as you've got enough passive income.

Fascists tend toward a more rigid social caste system (ideologically) wherein being rich isn't enough to save you from state violence. That's a big part of its popular appeal, particularly when liberal institutions decay into kleptocracies.

Traditional Marxism tends toward the social egalitarianism that fascists can't stomach (race mixing, gender equality, and worker internationalism) while advocating full public ownership that liberal rent-seekers can't stomach.

So, in the modern political spectrum, liberals tend to be "centrists" who use their economic influence to rent out social egalitarianism. Fascists tend to be "right wing", advocating for those same private entities to purge themselves of unpopular social groups. And Marxists tend to be "left wing", advocating for an abolition of rents and a full egalitarian economy.

But if you go back a century (or move over to a country that's more left or right leaning) the colonial era monarchies and theocracies end up forming the right-wing pole, while fascists join liberals at the social center, and Marxists join a much more lively native anarchist community that's in its last-gasp efforts to resist colonial occupation.

that's because liberalism in Europe is mainly "liberty" for rich people to do what they want

The US is such a right wing country that liberals are the mainstream left. In Europe, liberals are centrists and they aren't further to the right than American libs.

It's extremely frustrating hearing this repeated so often here.

It's fine if this is the colloquial definition you're used to hearing and using, but this is certainly not the way it's used outside of American politics and pretending like it's the only use comes off as both ill-informed and condescending.

When used derisively from the left, rest assured it is not referring to either of your adopted generalizations but a very specific ideology.

Liberalism has never meant "leftism in general." It has always been an ideology supporting the individual via private property rights. Neoliberalism is the modern form of it.

Liberalism was considered left when feudalism was right, but liberalism has never meant leftism.