> that would be a bad gym session. The goal is to push yourself. Not to injure yourself but to go until failure.

Umm. Actually, as far as I know, that's completely false. What you're describing is a bad way to train your body. If you're failing reps, you're training your body to fail. I.e. "one more rep" culture is misguided. You don't want stress or exhaustion hormones in your system. If your goal is enhancing your body, that is. Looking at my notes, my source is Pavel Tsatsouline #1399 episode on Joe Rogan's podcast. If you can get a hold of that podcast, it's very informative.

I won't comment on what you said about the mental aspect of failure.