WARNING: The following contains spoilers for My Hero Academia Season 5, Episode 5, "Operation New Improv Moves," now streaming on Crunchyroll, Funimation and Hulu.
The second round of the competition between Class 1-A and 1-B in Season 5 of My Hero Academia begins with Yaoyorozu, Tokoyami, Aoyama and Hagakure taking on Kendo, Kuroiro, Komori and Fukidashi. Along with Tokoyami and Kuroiro developing a rivalry, Kendo and Yaoyorozu go from being just friends to official rivals.
Class 1-A and Class 1-B have crossed paths on more than one occasion, especially during the Sport's Festival; however, Yaoyorozu and Kendo are perhaps the closest with each other. After the festival, they were both selected by Uwabami for an internship. Unfortunately, neither student got the experience they were hoping for, with the Pro Hero choosing Yaoyorozu and Kendo because they were cute enough to be in her commercial.
Since then, the two have often been lumped together. Yaoyorozu hadn't noticed this until it was brought to her attention, but Kendo is well aware of it, which further shows that Class 1-A has been disconnected from their other classmates since they've been at the heart of plenty of other crisis -- the USJ Attack, Bakugo's kidnapping, taking down Overhaul and much more. However, while Yaoyorozu was unaware of her and Kendo being lumped together, Hagakure isn't, noticing during the School Festival that the people cheering on Yaoyorozu were the same people cheering on Kendo.
Along with both prospective heroes sharing an internship, they also have similar roles in their classes. Kendo is Class 1-B's representative, keeping Monoma in line and acting as a big sister to her classmates. Yaoyorozu isn't Class 1-A's representative, but she acts like a big sister to many of her classmates, eagerly helping several of them study and working alongside Midoriya, Ida, Kirishima and Todoroki to save Bakugo.
While Yaoyorozu didn't notice these comparisons, Kendo is tired of them, especially since she considers Yaoyorozu's grades and Quirk better than hers. Because of this, Kendo wants to properly fight Yaoyorozu. Unlike some rivalries where there is tension between the two people, there appears to be no ill will between Yaoyorozu and Kendo. In fact, Yaoyorozu happily accepts this challenge, which isn't much of a surprise since Yaoyorozu often wants to bring out the best in her classmates, so if being Kendo's rival helps her break free of this comparison, the Everything Hero is more than happy to be the best rival she can be.
The two have yet to go head to head, but Kendo has already proven to be an impressive rival. Along with taking on the villains in the Forest Training Camp Arc, Kendo leads her team as they go against 1-A. They launch an initial attack using Kuroiro, and it almost leads to Aoyama's capture; however, when this fails, Kendo has a plan B up here sleeve that takes Yaoyorozu and Hagakure by surprise. Even from the limited footage for Episode 6, it appears Kendo is going toe to toe with Yaoyorozu, further cementing her as a remarkable rival for Class 1-A's vice president.