There has always been some confusion and arbitrary discussion about what the American political spectrum is. What defines the left and what defines the right. In many cases, there is an overlapping spectrum for libertarianism, socialism, liberal on social issues type stuff, but I don't use that stuff. It doesn't work for me from a framework standpoint. Anyone can arbitrarily define what they want "right" or "left" or "liberal" or "conservative" to mean. They are just labels. But if there is a continuum, I prefer the one I laid out below. But I do understand the concepts of the libertarian socialists and that the historical difference between was the difference in tactics between the anti-statist wing of the left (called libertarian) and the statist wing--which went in the socialist direction. But I do not find this to be relevant today.
In essence, the further left you go, the less power you have in few hands and the more power you have as broadly distributed as possible. The further right you go, the more it is concentrated in fewer and fewer hands. That's my metric.
Using the left as democratic, right as authoritarian and hierarchical is simply easier and clears up the muddy confusion over libertarians and socialism, liberals and the older political language. The language and discourse of modern politics is important because we power levelers are at a disadvantage for getting our message out, and the right wing has all of the advantage. We need to be quick with our message so it can be passed along quickly, without always needing such an extensive explanation.
Then there is the matter of labeling the opposition. I am growing fond of the term "right wing socialists" For starters, there is just a tiny splash of "national socialists" in the word, but most importantly, they have spent so much time and effort defining socialism as what they want it to mean through decades upon decades of business financed corporate propaganda--that the base of the right already has such an imprint of it to make it an extremely uphill, costly, and unnecessary battle to attempt to reclaim the word. The same applies to the word "Liberal".
The reason the term applies and fits so well is the bottom line economic reality that the right wing socialists very willingly, especially since Ronald Reagan's election in 1980, have taken the public money, and pooled it collectively and redistribute the wealth upwards. This has always been done, but it has been done at a more accelerated rate since Reagan's presidency. From a historical standpoint, it is the exception, not the rule to have power distributed towards the majority and away from the top. This a predictable consequence of living in a society that is dominated by privately financed corporate propaganda relaying precisely the opposite message: That the broader population is somehow in control and has somehow restricted the super special people who are not powerful because of their positions and experience in those positions but because of their inherent specialness.
To really change minds, you cannot operate on the terms of your opponents. They are setting the framework, and to play in to their frame and defend is not a winning strategy. They have already defined socialism and liberals. By using the updated, realistic term "right wing socialists" we mitigate their positioning by muddying the water--while building up the movement that defines the left: economic democracy and a broader distribution of power and decision making to the majority.
Attack and build, attack and build.