The specific human right is usually referred to as "freedom of association". You can read more here: https://en.wikipedia.org/wiki/Freedom_of_association
You need something more than freedom of association to justify unions, rooted in the recognition of bargaining disparities between employers and employees.
That's something the libertarian left and libertarian right surely agree on - minimising the application of the monopoly of force and all that.
So you assume both employers and employees can freely organize and associate. That's your starting point.
Now - we've decided that the right to join a union should be protected (it evens out an existing power imbalance) and that collusion to force down wages should be illegal (because it amplifies an existing power imbalance to the detriment of society at large)
We're moving away from areas where I'm confident I know what I'm talking about, but I think as a society we've decided that while anti-competitive laws do infringe on the rights of business leaders, we're trying to balance their rights with those of everyone else, and the laws are necessary to prevent a permanent class divide between business leaders who cannot be challenged, and workers under them. In the long run, allowing complete free association among CEOs would limit the freedoms of the rest of society.
Society is a constant project of balancing various conflicting rights, and this is one of many cases where we limit the rights of a few to defend the rights of many.