There have been several movies about time travel that can be considered illogical in their portrayal of the concept. One movie often cited for its illogical handling of time travel is "The Butterfly Effect" (2004), directed by Eric Bress and J. Mackye Gruber. While the film explores the intriguing idea of changing the past to alter the future, it introduces numerous inconsistencies and paradoxes.
In "The Butterfly Effect," the protagonist can travel back in time and change events that occurred during his childhood. However, each change has unintended consequences, creating a new alternate reality. These changes often seem arbitrary and illogical, with the protagonist acquiring new memories and abilities that were not present in the original timeline.
The film presents a nonlinear narrative that becomes increasingly convoluted as the protagonist attempts to "fix" the past. The inconsistent rules of time travel and the lack of a clear cause-and-effect relationship between actions and their consequences make the movie illogical from a time travel standpoint.
It's worth noting that illogical aspects in time travel movies are not uncommon, as the concept itself is highly complex and often defies our understanding of physics. However, some movies take more liberties with logic and causality than others, and "The Butterfly Effect" is frequently mentioned in discussions about illogical time travel films.