Some days we don't feel like training. I think some days we need to take time off if we are not feeling it. But, sometimes I believe we should push through to get the workout in. The answer to this depends on many factors and you will need to make it yourself. One thing you should not do is, train hard when you are overtrained.
A good tool to use is the broad jump. I usually do a broad jump test before my workouts to tell what the condition of my nervous system and body is. If you are overtrained, you won't be able to achieve your regular broad jump numbers. Days like these, it might be better to just do foam rolling followed by some light cardio. You can probably do some lifting also. I would not suggest doing heavy plyometrics or intense circuits if you are overtrained. No workout program is perfect and there are numerous factors that contribute to an athletes recovery. If your trainer creates a schedule for you, it is not possible for him to know how well you will sleep some nights or the stressful events you will encounter which will all effect your recovery. Tools like this should be utilized throughout athletic programs in order to tell if you are ready for a heavy training day. This method can prevent injuries. No need to beat the dead horse. We should train hard but also smart.