The ability to recover is essential in any form of training. Letting the body repair itself when it needs to is a means to build and rise within your being. Push too hard all the time without truly resting can kill you more than you'll believe. The body does grow stronger but in order for that to happen you need to give yourself a break.
I don't believe in "rest" days in the sense where you don't do anything on a non training day but use those those for reflection and what I call Recovery Workouts; training sessions that aren't vigorous and builds your energy from within. You can do Tai Chi, Qi Gong, Bua Gua or whatever internal arts you wish to practice, as long as you're keeping the blood flowing in a relaxed state you can possibly recover faster.
I believe in the power of healing whether it's from physical injuries or brain trauma or emotional imbalances. It takes practice but there ways to heal yourself. Exercise is great but also learning how to rest and program yourself into a meditative state that eases your well being and other things. I like resting my body for a day after a hard workout or if I get so worked up I just train until my body is ready to shut down and my body can rest. Be productive and not violent about finding ways to rest and let your body take care of itself both internally and externally.
The real strength is not in your muscles but in your mind. When you combine the mind/muscle connection as if they were one and the same, you are capable of doing many things. If your mind is full of stress and negativity your body will follow and it's not pretty; however the same can be said about the body, if it becomes too jittery and you're all over the place and your focus isn't in the right state of mind, your brain can turn on you and bring those neurons into that level of stress that can lead to inflammation, heart problems, physical injuries, low self-esteem and could bring harm onto yourself or others if you're not careful. Give yourself the opportunity to rest and recuperate so you can function at your very best. Training is not always trying to be the strongest or who can outlast who in the gym and it's definitely not about pushing your body to the limit every single day. When you have the amount of recovery you need, your focus shifts and your strength can reach new levels. Rest doesn't always mean sleeping 10 hours a day but being able to take the time and let yourself breathe and get into that relaxed state. Cool things happen when you are rested.