Centromere-drive is a process where centromeres compete for transmission through asymmetric "female" meiosis for inclusion into the oocyte. In symmetric "male" meiosis, all meiotic products form viable germ cells. Therefore, the primary incentive for centromere-drive, a potential transmission bias, is believed to be missing from male meiosis. In this article, we consider whether male meiosis also bears the primary cost of centromere-drive. Because different taxa carry out different combinations of meiotic programs (symmetric + asymmetric, symmetric only, asymmetric only), it is possible to consider the evolutionary consequences of centromere-drive in the context of these differing systems. Groups with both types of meiosis have large, rapidly evolving centromeric regions, and their centromeric histones (CenH3s) have been shown to evolve under positive selection, suggesting roles as suppressors of centromere-drive. In contrast, taxa with only symmetric male meiosis have shown no evidence of positive selection in their centromeric histones. In this article, we present the first evolutionary analysis of centromeric histones in ciliated protozoans, a group that only undergoes asymmetric "female" meiosis. We find no evidence of positive selection acting on CNA1, the CenH3 of Tetrahymena species. Cytological observations of a panel of Tetrahymena species are consistent with dynamic karyotype evolution in this lineage. Our findings suggest that defects in male meiosis, and not mitosis or female meiosis, are the primary selective force behind centromere-drive suppression. Our study raises the possibility that taxa like ciliates, with only female meiosis, may therefore undergo unsuppressed centromere drive.