Brain, the most important component of the central nervous system (CNS), is a soft tissue with a complex structure. Understanding the role of brain tissue microstructure in mechanical properties is essential to have a more profound knowledge of how brain development, disease, and injury occur. While many studies have investigated the mechanical behavior of brain tissue under various loading conditions, there has not been a clear explanation for variation reported for material properties of brain tissue. The current study compares the ex-vivo mechanical properties of brain tissue under two loading modes, namely compression and tension, and aims to explain the differences observed by closely examining the microstructure under loading. We tested bovine brain samples under uniaxial tension and compression loading conditions, and fitted hyperelastic material parameters. At 20% strain, we observed that the shear modulus of brain tissue in compression is about 6 times higher than in tension. In addition, we observed that brain tissue exhibited strain-stiffening in compression and strain-softening in tension. In order to investigate the effect of loading modes on the tissue microstructure, we fixed the samples using a novel method that enabled keeping the samples at the loaded stage during the fixation process. Based on the results of histology, we hypothesize that during compressive loading, the strain-stiffening behavior of the tissue could be attributed to glial cell bodies being pushed against surroundings, contacting each other and resisting compression, while during tension, cell connections are detached and the tissue displays softening behavior.