The electronic configuration of Fe²⁺ and Mn²⁺ ions are as follows:

Fe²⁺ is [Ar]¹⁸ 3d⁶.

Mn²⁺ is [Ar]¹⁸ 3d⁵. As it is known the half and completely filled orbitals have more stability. Hence, Mn with (+2) state has a stable d⁵ half- filled electronic configuration due to which Mn²⁺ resists to oxidise to Mn³⁺. We can find that, Fe²⁺ has 3d⁶ configuration and by losing one electron, its configuration can change to a more stable 3d⁵  half- filled electronic configuration. Therefore, Fe²⁺ easily gets oxidized to Fe⁺³ oxidation state.