Document reranking is a key component in information retrieval (IR), aimed at refining initial retrieval results to improve ranking quality for downstream tasks. Recent studies--motivated by large reasoning models (LRMs)--have begun incorporating explicit chain-of-thought (CoT) reasoning into LLM-based rerankers. However, the effectiveness of such reasoning for ranking tasks remains underexplored. In this work, we present the first systematic study of reasoning in reranking across both pointwise and listwise settings, under both supervised fine-tuning and reinforcement learning. Using diverse benchmarks, including reasoning-intensive datasets (BRIGHT) and standard IR benchmarks (BEIR), we find that reasoning-augmented rerankers consistently underperform their direct counterparts that predict rankings without CoT, despite substantially higher inference costs. Our analysis reveals three core limitations: (i) in pointwise rerankers, reasoning breaks calibration and biases models toward the positive class, raising TPR but lowering TNR, which inflates false positives and degrades ranking in negative-dominant pools; (ii) in listwise rerankers, reasoning improves in-domain fit but increases variance and fails to generalize out-of-domain, even when reinforcement learning shortens rationales; and (iii) overall, directly fine-tuned rerankers remain more stable, effective, and robust. These findings challenge the assumption that explicit reasoning is universally beneficial for reranking. We conclude by highlighting future directions, including calibration-aware scoring for pointwise rerankers and the design of concise, targeted reasoning strategies to mitigate overfitting and overthinking in listwise rerankers.