As discussed in some comments, the question is slightly unclear. One reading of it is that it's asking to list laws that exempt unions from anti-trust provisions. On another reading of it, the question is asking for an explanation why such [law] exemptions were made for unions. Below I try to answer the latter from the viewpoint of some economics theory.
It is a/the [US] right wing view to describe unions as a labor cartel. E.g. heritage.org says something like that:
Unions function as labor cartels, restricting the number of workers in a company or industry to drive up the remaining workers' wages.
So it's probably something like that that motivated the question.
The top-voted answer claims that labor market don't exist. That's an extremely Marxist viewpoint actually. (So I guess we've got a battle of the extreme viewpoints here.) A more reasonable/centrist point that is that perfect or free labor markets seldom exist, due monopsony-kind-of power that companies often have. For instance, we can read in an OECD paper:
The academic literature has focused on two broad classes of bargaining strategies. In the so-called “right-to-manage” model (Leontief, 1946), unions bargain exclusively over wages, leading to lower employment relative to the perfect competition benchmark. Union members, usually referred to as “insiders” in this literature, are viewed as gaining at the cost of “outsiders”, unemployed individuals or individuals in vulnerable jobs not covered by collective bargaining (Lindbeck and Snower, 1986). The cause of the presumed inefficiency is that employment is not accounted for in the negotiations. This could have the additional downside of reducing the resilience of the labour market against adverse macroeconomic shocks.
In practice, however, unions might not only be concerned about wages but also employment and macroeconomic resilience. This has motivated the “efficient bargaining” model (McDonald and Solow, 1981). Furthermore [...] the insider/outsider theory is not backed up by much empirical evidence.
The effect of collective bargaining depends also on the structure of the market and the degree of competition. With perfect competition in product and labour markets, raising wages above the market equilibrium wage induces unemployment. However, when product market competition is imperfect (i.e. when firms have some degree of monopoly or oligopoly power), higher wages may not induce greater unemployment but be simply the result of workers appropriating a greater share of the rents. Moreover, in imperfectly competitive labour markets, higher bargaining power and higher wage floors can increase employment. This would be the case in the presence of [labor market] monopsony power, which enables firms to offer wages below the market wage, for example because workers have limited opportunities to change their employer or would incur high costs if they did so.
So that's some more mainstream economics thinking reasons to allow labor unions. It's difficult to provide a nutshell answer to the "why" question across different jurisdictions though, as the localized reasons could be much more idiosyncratic.
But empirical data supports the idea that unions, especially of blue collar workers, increase rent sharing. (The right-wing view probably being, of course, that all the economic rent should go the firms/employers, albeit they don't phrase it this way.) Similar notes from the Economist:
When economists argue that unions impose economic costs, they typically assume that markets are competitive. Across much of the American economy that is not always the case. Sometimes one or a few big employers dominate local labour markets, and can thus impose below-market wages on vulnerable workers, a condition economists call “monopsony”. In recent testimony in a congressional hearing on antitrust issues, Kate Bahn of the Washington Centre for Equitable Growth, a think-tank, noted that though wages in manufacturing industries are close to the level one would expect in competitive markets, those in some others, like health care, are not. For workers frustrated by stagnant pay, a work stoppage may be the only way to determine if an employer is constrained by competitive markets or abusing its market power.
In the latter case, interventions by unions could prove economically useful. In a paper published last year, Mark Stelzner of Connecticut College and Mark Paul of the New College of Florida, argued that in the presence of monopsony power, collective bargaining can reduce the rents collected by dominant firms and increase economic efficiency.
If you want a more left-leaning answer than OECD or the Economist would provide (but still not as Marxist as the top-voted answer), some EPI article says:
“monopsony power” is often a confusing term to even the most savvy economic writers and researchers, and too often it is used only to describe markets that are concentrated (i.e., where there are relatively few employers). Market concentration can indeed suppress workers’ wages, but employer power exists even in markets with lots of employers. [...]
In competitive markets in economics textbooks, both employers and employees lack power. But in real-world labor markets, employers rarely lack for power, and our strong view is that policymakers should care more about balancing labor market power between employers and workers than about trying to create labor markets that are competitive in the textbook sense of the word. [...]
Policymakers must be committed to working on every available margin, including restoring genuine full employment as a macroeconomic policy priority; reforming labor law so that workers who want to form a union to collectively bargain to improve their wages and working conditions are able to do so; raising the minimum wage; and strengthening enforcement of labor standards and workplace civil rights laws. [...]
Some economists and policymakers might express unease at the view that the downsides of one deviation from “competitive” markets (either labor market frictions or market concentration or some other source of employer power) should be countered by introducing another market imperfection (e.g., unions or a binding minimum wage). But this unease is unwarranted. The “theory of the second best” clearly argues that once markets depart at all from perfect competition, efficiency may well be increased by further departures. For example, in the case of monopsony power in low-wage labor markets, legislated minimum wage increases can potentially move wages closer to efficient levels and increase employment.
So that would be the "moderate left" answer why unions are permissible.
Also, labor unions are sometimes a cartel with the participation of the employers as well (ahem Germany):
In countries where co-ordination works well, it tends to be strongly supported by employer associations since it moderated wage growth and trade unions since it ensured high levels of employment. To be effective, co-ordination requires strong and self-regulated social partners as well as effective mediation bodies.
If you want something even more to the left than that... here are some arguments from the Teamsters' heterodox economists: they basically think all anti-trust measures are utopian. And that labor cannot be a commodity for social & moral reasons. (It's more or less the argument from the top-voted answer.)
Unions are dubious about antitrust as applied to businesses. John Kenneth Galbraith's somewhat vulgar characterization: that antitrust policy is "Just a fart in a windstorm" is an apt characterization (Galbraith and Salinger, 1978, p. 40). The neoclassical
economists liked antitrust because it matched with their ideal of perfect competition.
However, antitrust is like a finger in a failing dike. Behind the dike are the massive
flows of the historical economic process. In this process the large and powerful multinational corporations get larger and more powerful. In a sense, capitalism is a race to see who gets the monopoly. Competition has winners, and those winners tend to keep
winning as they gain more power. Surely no one wins permanently, for new technologies buffet even the large and powerful. However, antitrust seems hopelessly utopian in
the face of the powerful historical trend toward concentrated economic power. [...]
Textbook economics portrays competition as almost universally good. But to the
union economist, competition can have some very perverse effects. Competing firms
have a powerful incentive to find ways to shift costs on to society. Thus, in the absence
of protective legislation, companies will choose not to bear the costs of cleaning up
pollution caused by their production processes. Private enterprise creates similar social
costs for labor (Kapp, 1975). [...]
What unions seek to do is remove wages, benefits, and working conditions from
competition. We seek to make employers pay a full social cost wage. We do this because
we know that if firms compete on the basis of low labor costs, workers will deteriorate
or the community at large will pay the social costs. [...]
Frictions predominate in the labor "market" and attempts to remove those frictions can be quite harmful. For example, because we have ties to the community and
family, we are much less mobile than commodities, and we are not necessarily fond of
the idea that markets would be more efficient if we were more mobile. Labor is also
highly perishable, and must be sold even when market conditions are unfavorable. For
if I do not sell my labor today, it is lost, unlike nonperishable commodities that are
more easily held off the market for a better price.
Perhaps most importantly, labor is human beings. Humans are not inanimate or
passive. We have wants and desires, complex motivations, and a need for meaning in
our lives. Whereas it is quite acceptable to treat a commodity as a means to an end, it
is generally thought to be immoral to treat a human being as a means to an end.
Polanyi labeled labor a "fictitious commodity." The capitalist utopians tried to
convert labor into a commodity, even though it was not produced for sale and was really
human beings. Workers did not wish to be commodities and reacted to protect themselves.
Utopians view unions as an interference in the working of the market, for free
markets cannot properly self-adjust with unions gumming up the gears of exchange.
However, unions are an inevitable result of the capitalist process, because society must
necessarily react against the market to protect itself. Unions are not the only such protection. Nature is also not a commodity, and the environmental movement is an attempt
by society to protect nature from being subordinated to the market.
Antitrust is a utopian attempt to restore a perfect competition that never existed and
cannot exist without destroying society. This should not be read to argue that all competition is bad. It is merely to argue that it needs to be restrained, that it needs to take place within a web of rules that assures the protection of human society. Applying antitrust to unions would not restore a system that cannot be restored. It would merely create a system in which business was able to dominate labor.
More jokingly, you can ask why allow people to create or participate in cartels known as political parties. After all, once in power, they can vote/legislate themselves somebody else's [tax] money. And if people are allowed to collude/cartel that way (ultimately promoting their economic and other interests), why shouldn't corporations get to vote too? (Or simply allow dollars to vote?)
The (final) point I'm trying to make here is that the legal fiction that "legal persons" = "natural persons" can only go so far... I'm saying this because it's fairly standard in economics-related laws (e.g. Mexico's) to define "Economic Agent [as] any natural or legal person [...]" and then stipulate that "Absolute monopolistic practices are considered illegal [...] amongst competing Economic Agents, which have as their purpose the effect of any of the following [...] To fix, raise, co-ordinate or manipulate the sale or purchase price of goods or services supplied or demanded in the markets;")
So if people band in a political party that wants to raise the minimum wage, that would be illegal according to a strict reading of such a law. (As pointed out by Rick Smith's answer, in the US the contradiction was noted and the Sherman Act was amended in 1914 to allow unions. Perhaps Mexico does have some similar overriding provision somewhere else in their legislation, I don't know for sure.)