We studied ferromagnet/superconductor/ferromagnet trilayers based on ${\text{La}}_{0.7}{\text{Ca}}_{0.3}{\text{MnO}}_{3}$ manganite and ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) high-${T}_{c}$ cuprate with magnetoresistance and magnetization measurements. We find an inverse superconducting spin-switch behavior, where superconductivity is favored for parallel alignment of the magnetization in the ferromagnetic layers. We argue that this inverse superconducting spin switch originates from the transmission of spin-polarized carriers into the superconductor. In this picture, the thickness dependence of the magnetoresistance yields the spin-diffusion length in YBCO as 13 nm. A comparison of bilayers and trilayers allows ruling out the effect of the stray fields of the domain structure of the ferromagnet as the source of the inverse superconducting spin switch.