In the series "Blue Lock," the rivalry between Yoichi Isagi and Rin Itoshi develops as they both compete to become the top striker in the Blue Lock program. Their contrasting playing styles and personalities create tension between them, leading to intense battles on the field as they strive to outperform each other and prove themselves as the best striker. This rivalry pushes both characters to improve and grow as players, making their interactions compelling and exciting to watch.