There is lots to recommend "don't give up". But it also has to be tempered with "Stop if it hurts". You'll get fit/strong/endurancy-faster if you can keep training tomorrow than if you have to spend three weeks icing your wrists and gobbling down NSAIDs.
EDIT: Leaving this up for posterity because why not. After re-reading your comment, I'm not convinced that we disagree. It's just that the whole thing becomes extremely nuanced once you start talking about things like: "I'm stopping doing e.g. chinups today so that I can do more tomorrow. I'm not giving up on my goal, I'm just altering the timeframe". Here it's not clear how you should interpret the "Don't give up" mantra.