What is it about the relationship between the Fe²⁺ and Fe³⁺ in magnetite that makes it diamagnetic?
Magnetite has a spinel structure with two types of $\ce{Fe}$ sites: octahedral and tetrahedral, respectively in green and orange below.



(in this structure, oxygen atoms are the small red balls).

This structure is called a spinel, with $\ce{Fe^{2+}}$ ion in tetrahedral coordination and $\ce{Fe^{3+}}$> ions in octahedral sites. The coupling between atoms from these two lattices are superexchange interactions, which result in an antiparallel alignment of spins. However, because the magnetic moments of the two lattices are not equal, their addition results in a net magnetic moment, even though they are of opposition alignment. This is called ferrimagnetism, and in practice most of its macroscopic properties are similar to ferromagnetism, though they stem from a completely different microscopic magnetic ordering.