This paper investigates the cavity–magnon steering and qubit–qubit steering of a hybrid quantum
system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the
presence of their damping rates. The temporal wave vector of the system is obtained for the initial
maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes.
Additionally, the mathematical inequalities for obtaining the cavity–magnon steering and qubit–
qubit steering are introduced. The findings reveal that steering between the magnon and cavity
is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the
atom–field coupling improves steering from magnon to field, while reducing steering between the
two qubits. Moreover, increasing magnon–field coupling enhances and elevates the lower bounds of
qubit–qubit steering. Further, adding the damping rates causes deterioration of the cavity–magnon
steering and qubit–qubit steering. However, the steering persistence is slightly greater when damping
originates from the cavity field rather than the magnon modes based on the coupling parameters.