This study leverages deep learning to analyze sex differences in brain MRI data, aiming to further advance fairness in medical imaging. We employed 3D T1-weighted Magnetic Resonance images from four diverse datasets: Calgary-Campinas-359, OASIS-3, Alzheimer's Disease Neuroimaging Initiative, and Cambridge Center for Aging and Neuroscience, ensuring a balanced representation of sexes and a broad demographic scope. Our methodology focused on minimal preprocessing to preserve the integrity of brain structures, utilizing a Convolutional Neural Network model for sex classification. The model achieved an accuracy of 87% on the test set without employing total intracranial volume (TIV) adjustment techniques. We observed that while the model exhibited biases at extreme brain sizes, it performed with less bias when the TIV distributions overlapped more. Saliency maps were used to identify brain regions significant in sex differentiation, revealing that certain supratentorial and infratentorial regions were important for predictions. Furthermore, our interdisciplinary team, comprising machine learning specialists and a radiologist, ensured diverse perspectives in validating the results. The detailed investigation of sex differences in brain MRI in this study, highlighted by the sex differences map, offers valuable insights into sex-specific aspects of medical imaging and could aid in developing sex-based bias mitigation strategies, contributing to the future development of fair AI algorithms. Awareness of the brain's differences between sexes enables more equitable AI predictions, promoting fairness in healthcare outcomes. Our code and saliency maps are available at https://github.com/mahsadibaji/sex-differences-brain-dl.