Metathesis reactions, including alkane, alkene, and alkyne metatheses, have their origins in the fundamental understanding of chemical reactions and the development of specialized catalysts. These reactions stand as transformative pillars in organic chemistry, providing efficient rearrangement of carbon-carbon bonds and enabling synthetic access to diverse and complex compounds. Their impact spans industries such as petrochemicals, pharmaceuticals, and materials science. In this work, we present a detailed mechanistic study of the Re(V) catalyzed alkyne metathesis through density functional theory calculations. Our findings are in agreement with the experimental evidence from Jia and co-workers and unveil critical factors governing catalyst performance. Our work not only enhances our understanding of alkyne metathesis but also contributes to the broader landscape of catalytic processes, facilitating the design of more efficient and selective transformations in organic synthesis.