Maybe don’t train through, but consider training around, injuries.
From time to time we get banged up. We’re human.
If you’re training to increase your general fitness with overall health, then you shouldn’t be getting banged up in the gym. I understand that fluke accidents do occur, but more often an injury comes from something outside of the gym. Things like rolled ankles, work related injuries, and back strains are fairly common.
The question that then comes up is “How long should I stay away from the gym?”
For arguments sake we’ll assume your injury isn’t very serious and your doctor is ok with you continuing activity. If you’re ever unsure or are uneasy about an injury, go see your doctor.
More often than not, the answer for recovery is not to halt all activity. This may seem counterintuitive, but training the uninjured side of the body will have a positive effect on the side that you’re resting. So, keep showing up to the gym. Work with a coach and set a plan of attack to train around those setbacks. It’s much easier to keep your momentum going than it is to stop completely and then restart.