What moves the chromatids around during cell division?

Spindle fibres move the chromatids around during the cell division.

Explanation:

Spindle fibres are made with proteins which arise from the centrioles during "Mitosis or Cell division". Spindle fibres bind to the kinetochore protein present on the centromeres of each chromosomes from the two opposite ends during prophase and held them at the metaphase plate during metaphase stage. During anaphase spindle fibres pull the sister chromatids in opposite of the opposite poles and start to disappear in telophase.