First I'll rule out the idea that there could be a conclusive reason not to have certification. That means a reason that can't be outweighed by anything - like, if it went against some ultimate value. I'm going to assume that certification, if it is wrong, is wrong in virtue of the risks outweighing the benefits, not because it's inherently immoral.
There are two interdependent strains to the argument. One is that regulation of all kinds is always bad, that is to say, it has bad consequences of some kind. Specifically in this case, that it fails to ensure only good trainers can train dogs, and that it takes power away from the public, or really, the market. Second is the claim that because there is debate over what classes as science-based and as ethical in dog training, a central authority would be forced to impose a controversial value judgement on trainers and the public. Such an imposition would go beyond the mandate of any such authority, therefore, we should not centrally regulate dog training.
I will argue that although there are grains of truth in both claims, neither amount to a convincing argument for reversing the decision to regulate. They merely draw attention to the need for caution in developing the institution and setting the standards.
1. Regulation Restricts Choice
The situation right now in the USA is that there is no central regulation but a lot of different certification bodies and schools, all with different standards and all claiming to be a metric to set some trainers above others. Why might this be preferable to a centralized regulatory body? One reason is that it provides choices for individual dog owners, and more choice is good. Individuals in need of training certainly do have a lot of choice. But the question of whether this much choice is always good is still open; if we assume choice is valuable in part because of a link to a more important good like wellbeing, then being able to choose between dog trainers is only valuable to the extent that it does in fact allow individual dog owners to choose the best fit for them and their dog.
I would argue that there is too much choice with too little guidance, and that marketing is unduly influential in prejudicing that choice. Properly implemented, regulation would provide a basic standard; the choice would be between educated, qualified professionals. The benefits it would provide outweigh the cost of restricting the number of trainers between which a dog owner can choose. All responsible dog owners want to choose a high-quality trainer who will effectively train their dog; stripping out the charlatans, abusers and delusional people isn't going to cause a decrease in their welfare or that of their dog.
2. Regulation Won't Promote Quality
The second objection is that for all its lofty aims, regulation has shown itself to be unsuccessful in stripping out the worst of the worst. This is usually explained as an analogy. We can all remember that one schoolteacher whose lessons we always dreaded or who seemed to teach us nothing at all. Not all teachers are equally good - some are terrible - but all teachers are subject to the same regulatory standards. If teaching quality isn't correlated with regulation, we have no reason to assume dog training quality will be either. Regulation won't succeed in its stated aims.
This is a strawman, however. Nobody is claiming that regulation in itself will purge training of people who aren't very good at it, or who can pass their exams and then proceed as if they never had an education. Regulation isn't a silver bullet, but it could be one important barrier to entry. Moreover, with the best approach to regulation would come a system of formal complaints, so those animal abusers and ineffectual instructors could be subject to sanctions.
This argument is often packaged with a related claim, that market forces or "the power of the public" provides a more effective way to sort the wheat from the chaff than top-down regulation. This relies on a rose-tinted view of how individuals get their information about dog training. With clever marketing, coupled with a lack of public knowledge about alternatives, a bad trainer can convince people she's fantastic. Cesar Millan is doing pretty well for himself despite his recent Teutonic oversight.
3. Regulation Can Never Be Neutral On Ethics
This objection is less about the theory of whether regulation is a bad thing per se, and more about whether dog training in particular ought to be steered by any one group of people.
The "training wars" show us that there is extreme disagreement about what counts as ethical, humane training. "Force free" has been labelled as a lifestyle choice, and P+ is often unreflectively compared to animal abuse. On the other side, trainers who use corrections claim their position is mischaracterized because their techniques are poorly understood. Both sides feel oppressed and victimized by the other. In this climate, how can we hope to create a judicious, clear-eyed group of regulators? Is dog training the kind of enterprise where making any judgements on ethics is likely to lead to such bad consequences that regulation is not worth any potential benefits it could bring?
First off, it is clear that we don't want regulatory bodies to be dead neutral on ethically-sensitive matters. Euthanasia, abortion, stem cell research, removing children from their biological parents, all highly sensitive and divisive issues and all subject to guidance that comes both from ethics and law. The fact that a regulatory body has to come down on some issues to do with what it is regulating, however, does not mean they are committed to binary pronouncements on all such issues.
Nevertheless, there is a grain of truth in this worry. Ethical pluralism is an important commitment in a broadly liberal, democratic society and regulatory bodies ought to be hospitable to more than one view of what counts as ethical action. Putting a blanket ban on one style of training or one kind of tool in place risks alienating a lot of trainers and creating a backlash to the enterprise of regulation in the first place.
Furthermore, questions of what 'counts' as animal abuse are open to a degree of interpretation - proponents of electronic collars, for example, claim that their methods don't cause a significant impact on welfare when they are properly used. Biologists, psychologists, and philosophers still disagree on the theory of welfare, and there is not yet overwhelming scientific evidence that correctly-applied positive punishment meets the definition of abuse.
A good regulatory system would take into account ethical differences and try to minimize substantive judgements. In setting a standard of knowledge and skill, regulation could ensure that only trainers who demonstrate a commitment to animal welfare and knowledge of animal behavior can train professionally. There is no need to come down one way or the other on issues like the use of electronic collars.
Psychotherapy could be an informative analogy. There are many different schools of psychotherapy with radically different approaches to their patients; many practitioners are vocal in their disagreements with some of their colleagues' chosen methods. Regulation exists, however, and differences of opinion are preserved. The regulation of dog training could be like the regulation of psychotherapy, with a plurality of methods and different basic assumptions united by a standard of professional competence that conceptually functions as a lowest common denominator.
Efficacy could play the same role in dog training as professional competence does in psychotherapy - define efficacy and you have a standard of competence. We could design regulation around the potential to be an effective trainer; what sort of basic knowledge would someone need to train effectively? With this, the professional bodies we see now like PPG could still play a role, that of setting guidelines for best practice within their chosen theory.
The benefits of regulation, for dog trainers, owners, and dogs, are clear: overall higher standards of competence, a framework for dealing with complaints and less reliance on marketing. Provided it didn't fall victim to mission creep or the efforts of lobbyists, a regulatory system could allow trainers of all schools to uphold the same standards of competence. And competence, with its attendant benefits to dogs and owners, is paramount for all trainers.