Let me state up front that I reject any division of libertarianism into left and right wings. To do so is nearly akin to dividing it into high and low, yellow and blue, or round and triangular versions. Yes, there are quite a few more or less enthusiastic supporters of the division; indeed, reading some of them suggests that they have a lot invested in this effort. However, I find what they are embarking upon, if not outright incoherent, then certainly confusing and a waste of good energy and time that could be devoted to more important elements of the task of advancing the cause of human liberty.
Combining libertarianism with elements of the Right or the Left defeats the purpose of conceptual clarity about a certain broad political topic. Historically, neither the Right nor the Left has shown a sustained, uncompromising loyalty to individual human rights to life, liberty and property, while classical liberalism and especially libertarianism is exactly about such unwavering loyalty, one that requires the proverbial eternal vigilance.
By its nature libertarianism is about political liberty for all individuals to do whatever is peaceful or non-aggressive, including acquiring and holding property or valued items either found in nature or obtained through free trade and inheritance.2 Claiming that libertarianism can include more or less severe limits on the right to private property − imposed by public policy and law − as Left-libertarianism does, simply renders the view indistinguishable from what social democrats and welfare statists propose. It reminds one of market socialism, arguably another oxymoron.