Knowledge Distillation (KD) has been validated as an effective model compression technique for learning compact object detectors. Existing state-of-the-art KD methods for object detection are mostly based on feature imitation, which is generally observed to be better than prediction mimicking. In this paper, we show that the inconsistency of the optimization objectives between the ground-truth signals and distillation targets is the key reason for the inefficiency of prediction mimicking. To alleviate this issue, we present a general and effective distillation scheme, called CrossKD, which delivers the intermediate features of the student's detection head to the teacher's detection head. The resulting cross-head predictions are then forced to mimic the teacher's predictions. This manner relieves the student's head from receiving contradictory supervision signals from the annotations and the teacher's predictions, greatly improving the student's detection performance. On MS COCO, with only prediction mimicking losses applied, our CrossKD boosts the average precision of GFL ResNet-50 with 1x training schedule from 40.2 to 43.7, outperforming all existing KD methods. In addition, our method also works well when distilling detectors with heterogeneous backbones. Code will be made publicly available.