After decades of wolves being absent from the American Rockies, a push began to reintroduce wolves into their historic range throughout the Rockies. This push had two primary motivations. First, there are a lot of nature lovers out there (myself included) and popular culture has firmly established the wolf as a symbol of nature and of untamed wilderness. It's understandable that people would want to restore these majestic looking canines to their once and former glory. This first motivation is likely to be the one that you'll hear about in any public debate of the topic, even though it's fairly childish, simplistic, and easily dismissed.
The second motivation is considerably more sound from a logical perspective and is the one I recommend you consider when thinking over these issues. The natural world is a horrendously complex entity. It's what we engineers call an a highly uncertain and nonlinear system. The "highly uncertain" part is pretty self-explanatory, the response of the system depends on hundreds of independent factors like the birth rates of all the various species, weather patterns, infant mortality, plant productivity, etc. A precious few of these parameters can be measured to a reasonable accuracy, and even if you had unlimited funding and could determine all the requisite numbers for this year, you have no reason to expect that next year's numbers would be the same.
The "nonlinear" part is a little more interesting. Linear systems are the nice, friendly ones that most of us deal with in school. A 5% change in the input of a linear system will cause a 5% change in the output of that system. A 1% input shift moves the output 1%, and so forth. Nonlinear systems on the other hand are pesky beasts by comparison. The inputs and outputs of nonlinear systems are not so cleanly linked. A large change in the input could produce no noticeable change in the output, or conversely, a minute input shift could cause the system to go careening out of control towards a highly undesirable outcome.
So, now that I've scared off half my audience with two paragraphs of technobable, you few brave souls who have persevered to this point in the post can now understand just how big of a deal it is when we describe a system as "highly uncertain and nonlinear". We're essentially saying that we can give it our best shot, but we're never going to be able to control the system or even predict its outcomes with a high level of confidence.
In other words, we should be exceptionally careful with any tweaking that we do to ecological systems. Because, no matter how advanced our models get, we will never know ahead of time whether or not we will be able to accurately predict the many effects of that tweaking.
Nature has been regulating its systems for billions of years before we got here and did just fine, so that is always the safer option. We should avoid attempts to exert control over ecological systems whenever possible, and when that option is not available (as is often the case) we should look to minimize the extent of our intervention. Herein lies the strongest argument for the reintroduction of apex predators into ecosystems where we have exterminated them. The removal of such a major piece of the ecological puzzle in undeniably an extensive intervention and, for the reasons outlined above,any such intervention should be avoided. The safer course of action over the long term is to maintain the ecosystem in a state as close as possible to its historical condition.