The rivalry between Boruto and Iwabee Yuino in the anime "Boruto: Naruto Next Generations" begins with a clash of personalities and ideals. Iwabee, who is more serious and dedicated to his studies, initially clashes with Boruto's carefree and rebellious attitude. However, as they spend more time together and get to know each other better, they start to develop a mutual respect and understanding. Their rivalry eventually turns into a friendship as they support each other in battles and challenges, working together towards common goals. Overall, their dynamic adds depth and character development to the story.