Karyotype, chromosome number and composition, is a basic characteristic of species and its changes are frequently associated with speciation. Karyotype conversion, from mostly telocentric (centromere terminal) to mostly metacentric (centromere internal), typically reflects fixation of Robertsonian (Rb) fusions, a common chromosomal rearrangement that joins two telocentric chromosomes at their centromeres to create one metacentric. Fixation of Rb fusions can be explained by meiotic drive: biased chromosome segregation during female meiosis. However, there is no mechanistic explanation of why fusions preferentially segregate to the egg in some populations, leading to fixation and karyotype change, while other populations preferentially eliminate the fusions and maintain a telocentric karyotype. Using laboratory models and wild mice, we show that differences in centromere strength predict the direction of drive. Stronger centromeres, with higher kinetochore protein levels and altered interactions with spindle microtubules, are preferentially retained in the egg. Rb fusions preferentially segregate to the polar body in laboratory mouse strains when the fusion centromeres are weaker than those of telocentrics. Conversely, fusion centromeres are stronger relative to telocentrics in natural house mouse populations that have changed karyotype by accumulating metacentric fusions. Preferential chromosome segregation is predicted to depend on spindle asymmetry. We show that meiosis I (MI) spindles are asymmetric, with more stable microtubules (MTs) oriented towards the cortex. Based on our observations we propose a model in which a signal from the cortex induces MT asymmetry. We exploit Rb fusions to study mechanisms of meiotic chromosome segregation when erroneous kinetochore-MT attachments are recognized and destabilized. Improper attachments typically lack tension between kinetochores and are positioned off-center on the spindle. Low tension is a widely accepted mechanism for recognizing errors, but whether chromosome position regulates MT attachments is unknown. We show that proximity to spindle poles destabilizes kinetochore-MTs, and that stable attachments are restored by inhibiting Aurora A kinase at spindle poles. During the correction of attachment errors, kinetochore MTs detach near spindle poles to allow formation of correct attachments. We propose that chromosome position on the spindle provides spatial cues for the fidelity of meiotic cell division.