Why is it important to study logic in philosophy? One answer might be that logic teaches you correct reasoning, but that is not something that is unique to philosophy, as it's important in other fields as well (e.g. history, economics, physics, etc.), and those usually do not include any explicit study of logic.
In my experience, philosophy courses take the explicit, self-conscious formulation and evaluation of arguments (i.e., reasoning) more seriously than any other courses of study, with the possible exception of those math courses that emphasize proofs. Moreover, the breadth and depth of philosophical problems exceed those encountered in math. Therein lie the advantages of philosophy courses as compared to, say, math or economics courses. If you pursue philosophy, I think you'll discover that the standards of argumentative rigor expected in philosophy courses surpass -- sometimes by far -- the standards of rigor expected in any courses outside of math, and again they're applied to a much more varied, and often deeper, set of questions.