A thrust reverser for an aircraft propulsion assembly, this reverser including an outer structure movable between a closed position and an open position of two primary latches configured to lock the movable outer structure in the closed position. The movable outer structure includes an output end that is oblique with respect to the longitudinal central axis so as to orient the thrust laterally. In order to compensate the tilting moment of the movable outer structure, which results from this lateral orientation of the thrust, the primary latches are offset with respect to a median longitudinal plane passing through the longitudinal central axis of the reverser.