I dislike when governments get involved and starts forcing employees to join unions.
But if you want to unionize, you have that right. If the companies don't want to play ball, they can fire you and waste time and money trying to hire an all new workforce.
When you talk about giving unions as free associations, it's fair to ask whether companies should share the same rights -- if tech workers can get together and agree not to work without a pay rise, shouldn't tech companies be allowed to get together and agree not to increase pay?
I think if we're going to distinguish between those cases it should be on pragmatic grounds, because I don't think talking about principles (or any "natural right" divorced from the simple letter of the law) here is terribly useful.
So no companies should not share the same "rights", because that's called being anti-competitive. Labor unions are only capable of "exert[ing] anti-competitive influence" when unions have recruited every worker (probably for a good reason) or companies engage in union busting against workers who have done nothing wrong (except talk to a union). Don't want to deal with organizing employees? Don't sign a contract with them (the employee-employer relationship also granting companies a bunch of useful rights).
Fair point. You could also say it makes certain sense vis-a-vis the company shareholders (be it the founders, or stockholders) being "colluding" and "price-fixing" on the other end of the employment deal.