In neoclassical theory is said that the highest profit occurs when Marginal Cost equals Marginal Revenue, but this condition wouldn't be enough to determine the maximum if there were more than one. The fact that the maximum can be determined like this means that the uniqueness of the maximum derives from the assumptions of the theory? My professor said that the uniqueness is determined by the static nature of the theory, but this seems to me a little vague. How can it be explained in a more satisfactory way?
Mathematically, most neoclassical models assume that the profits are concave. This guaranties the uniqueness of the maximum. In economic terms, the Neoclassical theory usually assumes that the law of diminishing returns holds. Thus, the more you hire workers, the more you produce, but at a diminishing rate.
I am not so sure what your professor has in mind when he brings up the "static nature of the theory". There are many dynamic neoclassical models and most of them have a unique maximal profit that also arises from having an appropriate form of diminishing returns, i.e. concavity of the profit function.