Brain metastasis segmentation in MRI remains a formidable challenge due to diminutive lesion sizes (5-15 mm) and extreme class imbalance (less than 2% tumor volume). While soft-attention CNNs are widely used, we identify a critical failure mode termed the "over-segmentation paradox," where models achieve high sensitivity (recall > 0.88) but suffer from catastrophic precision collapse (precision < 0.23) and boundary errors exceeding 150 mm. This imprecision poses significant risks for stereotactic radiosurgery planning. To address this, we introduce the Spatial Gating Network (SG-Net), a precision-first architecture employing hard spatial gating mechanisms. Unlike traditional soft attention, SG-Net enforces strict feature selection to aggressively suppress background artifacts while preserving tumor features. Validated on the Brain-Mets-Lung-MRI dataset (n=92), SG-Net achieves a Dice Similarity Coefficient of 0.5578 +/- 0.0243 (95% CI: 0.45-0.67), statistically outperforming Attention U-Net (p < 0.001) and ResU-Net (p < 0.001). Most critically, SG-Net demonstrates a threefold improvement in boundary precision, achieving a 95% Hausdorff Distance of 56.13 mm compared to 157.52 mm for Attention U-Net, while maintaining robust recall (0.79) and superior precision (0.52 vs. 0.20). Furthermore, SG-Net requires only 0.67M parameters (8.8x fewer than Attention U-Net), facilitating deployment in resource-constrained environments. These findings establish hard spatial gating as a robust solution for precision-driven lesion detection, directly enhancing radiosurgery accuracy.