A mere Double Fusion stands no chance to a superior Triple Fusion No.37508462 Report Quoted By:
League battles are ran by two people with experimental Pokedexes called Pokevices given to them by the region's Professor (having a Pokevice makes them part of the league / important). They are double battles that end defeating the healed stronger Fusion of the two aces. Since you have a Pokevice too, after defeating a gym you connect with their two Pokevices to register how to fuse into the Fusion you defeated. Pre-evolutions of the two aces are found on opposite routes of the Gym's town / city. Agumon and Gabumon (pre-evolutions of the Champions' aces) are found in post game areas, a volcano and icy cavern respectively.
The evil team leader was actually a co-developer of the Pokevice but was removed from the project by the region's Professor due to not caring about the harmful stress a Triple Fusion puts on the Pokemon. The goal of the evil team is to create the pinnacle of Pokemon Fusion: Glicanstoise, the plot "legendary" of the game. Leading up to the battle against the evil leader using Glicanstoise, you had fought them three times previously that each ended with one of the Double Fusion possibilities. The fusees are eventually made to be the first Triple Fusion from a Pokevice enhanced by the evil leader that he calls the Pokevice Plus, but these developments also prevent it from unfusing. Fortunately if it relieves stress by battling, the Triple Fusion is not a problem. After defeating the leader who fused his three childhood Pokemon to pursue his curiosity of science he says you should take care of Glicanstoise, but Glicanstoise isn't just going to change sides. The leader understands what he says before Glicanstoise runs off, and you're told he went to their favorite childhood cave waiting for you to challenge him on an early route that requires the last HM / Ride / etc to access the challenge. This capturable rematch is stronger with a different good moveset your underleveled team can't do anything to yet.