We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0-1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree-Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the non-empirical choice of the mixing coefficient under ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other types of functionals like screened hybrids.