The Pokemon anime has created many mysteries that the show has yet to solve, and many fans enjoy theorizing on the answers to these questions. However, recent information surfaced from the original Pokemon anime writer that gives his take on one of the earliest mysteries surrounding Brock and Professor Ivy.
Professor Ivy came up during the Ash Ketchum's Orange League adventure, which is the second season of the Pokemon anime. Misty and Brock followed Ash to the Orange Archipelago, where Professor Oak asked Ash to pick up a unique Pokeball from the other Pokemon researcher. However, during the group's encounter with the professor on this errand, Brock does what frequently happens in the show and falls in love with the female professor.
Brock's attraction to Professor Ivy goes so far that he decides to stay back with her while Ash and Misty continue on to explore the region without him. After that Pokemon season's adventure, the three of them met up at Ash's house before embarking on the journey to Johto in the next season.
However, it was never explained why Brock left Professor Ivy, and when her name was brought up, Brock curls up in a ball and says not to speak her name. This unusual behavior has caused many fans to question what happened between them to make him react to her name in such a way. However, this has never been addressed in the show itself.
Takeshi Shudo, the original head writer of the Pokemon anime, seemed to have his own theories about what happened between the two characters. The information was written down in Pocket Monsters: The Animation, a book that he wrote before his death in 2010. In the book, Shudo says that he believes the reason for Brock's strong reaction to Professor Ivy's rejection is because she may be a lesbian.
When Brock is normally rejected throughout the Pokemon anime, he quickly moves on, but Professor Ivy's rejection has clearly stuck with him in a significant way. Shudo surmises that, if the Pokemon professor was only attracted to women, then the rejection may have hit Brock harder since he never had a chance with her to begin with.
While it would be nice to have some LGBTQ+ representation in a popular game-based, this theory shows problematic behavior towards non-heteronormative characters. Nothing Brock has done would be the reason for the rejection, while many other rejections he faces from other girls don't have that excuse, and he seems to take those well enough without lasting effects. However, the fan theory isn't confirmed, so this may not truly be the reason for the falling out between them.
Source: ComicBook Anime