How are chromatids correctly segregated during mitosis?
It's a spatial constraint.  As the DNA is replicated, the two resulting chromatids are kept stuck together by cohesin proteins.  The DNA sequence that corresponds to the centromere then coalesces the kinetochore.  It seems that the DNA-protein interactions at the centromeres creates a particular structure along the chromosome.  Since the two chromatids have their kinetochores pointing in opposite directions, when a spindle microtubule attaches to the kinetochore, it is nearly impossible for another microtubule from the same spindle to attach to the opposing kinetochore.