I have also struggled with the exact same question. A related question is, how could people considered radicals and revolutionaries in their day, if looking at their policy prescriptions, be considered generally conservative in modern american politics. Here is the conclusion I’ve come to.
A dictionary definition of a left-wing movement tends to support changes for a more equal and egalitarian society.
A dictionary definition of a right-wing movement tends to support preserve the existing order and tradition along with some kind of hierarchy.
Most people make the mistake of equating left-right with an ideology or group of policy positions. For instance, “Leftists support government intervention”, “rightists support war” would be 2 logical fallacies. To determine if a movement or person has more left or right wing tendencies, one must drill down into their reasoning and historical context.
A clear example might be about voting. In 17th century England, a person who believes that all men, but not women, are created equal and therefore should get to vote for parliament would be a leftist because that would be a change towards more equality. After all men won the right to vote for parliament, that position and reasoning would later become right-wing position and reasoning once the question of women voting for parliament is tackled as an issue.
For my two examples above. There is nothing inherently left or right about government intervention or even war. The thing that makes it left or right is the reasoning behind the movement or individuals supporting it. In the case of regulation, there is a right-wing Hamiltonian case for government intervention – the elite need to plan for the nation. There is also the more common progressive left-wing argument in that “big business” needs to be restrained. The same goes for war. A right-wing argument for war might be something like “that group isn’t like us and needs to be opposed for us to survive”. A left-wing argument for war might be something like “that group is being oppressed and needs to be saved”.
It is true that within a given nation and time period, right-wingers tend to support one ideology and policies more often than others and the same thing for left-wingers. And that is why people make the mistake of associating policies with being left or right.