Libertarianism literally started on the very far left - an anarcho-communist named Joseph Dejacque. Right libertarianism is about a century younger, and the main distinction is view on property rights, which left libertarians tend to see as oppressive government overreach. (Dejacque enthusiastically supported Proudhons famous 'property is theft')
Left libertarianism and right libertarianism agree on nearly everything. It's not like "left" and "right" which are effectively polar opposites.
Right libertarianism has an antitrust problem -- if the state establishes corporations and enforces property rights then corporations can become powerful enough to be de facto governments. Left libertarianism solves it by deleting property rights, which of course has its own drawbacks.
A middle ground that might work is to allow humans to own property but not corporations, because the largest accumulations of capital have always taken corporate form.
Obviously the non-purist can also solve it by having government-enforced antitrust laws.
