The stupidity hurts. Why is one half of the population murdering the other half? Are they in a competition for scarce resources? In that case, why keep both twins around at all? Why not selectively abort or turn to infanticide?
Furthermore, the ableist and eliminationist implications of this are disturbing, to say the least. If one twin has a disability and the other doesn't, there are many ways in which the twin without the disability could exploit the other's disability to kill him/her off. Has the author thought about the bias against disabled people inherent in her worldbuilding? To be clear, I have no problem with ableism in worldbuilding. I do have a problem, however, with ableist bias in worldbuilding done by an author without a grain of self-reflectiveness.
You know, if you really wanna run with this "kill your twin" premise, why not attack the inherent ableism head on? Give both twins disabilities. One could be a deaf person with agoraphobia and an anxiety disorder. The other could be a person with depression, narcolepsy and binge/purge syndrome. Then they could grow to be friends. Maybe they would even fall in love. They would decide that this whole "kill your twin" thing was, in fact, incredibly stupid and struggle to make their own lives in a society that a) expects them to try to kill each other and b) devalues people with disabilities anyway.
Man, that would be a much better story!