Due to IVF and genetic changes humanity only exist in the future as twins or multiple births. A self-proclaimed leader decides that the natural balance has to be restored by what he calls natural selection. The tormented genius “Daggy” Pollux fights against the execution of his love interest who’s been selected as the weaker one.

Good points made already, I'll only add that a logline needs to focus on the primary action, goal, and obstacle the main character faces.

Your logline mentions too much, yet at the same time, explains very little about the story and character motivations. You can cut the first two sentences and reword the third so it details the sequence of events which motivated the MC to take action, for example: After his fiance is selected for execution by the government, a [good main character description] must [take this action] to save her life.

Reading through the rest of the comments on this thread, it becomes clear that the story is more about the twins than the lovers so the above example is more of a structural guide at this point.