You may be interested to know that the field of psychology has studied quitting, and the findings are quite reassuring.
Take these two articles on “goal disengagement” (the fancy term for quitting) – they found that disengaging from a goal is beneficial to psychological wellbeing!
The importance of goal disengagement in adaptive self-regulation: When giving up is beneficial.
Wrosch, C., Scheier, M. F., Carver, C. S., & Schulz, R. (2003).
Adaptive self-regulation of unattainable goals: goal disengagement, goal reengagement, and subjective well-being.
Wrosch C1, Scheier MF, Miller GE, Schulz R, Carver CS.
To be more specific – they found greater wellbeing was associated with disengaging from a goal and re-engaging with a different goal. Here’s a flowchart from the first article I listed:
At the top of the flowchart it shows how sticking with an unattainable goal can lead to feelings of distress and futility, whereas disengagement (with re-engagement) can lead to an absence of distress.
So when someone tells you quitters never win, you can tell them SCIENCE begs to differ. Because I don’t know about you, but absence of distress sounds like winning to me!