-다 못해 means "unable to continue" - stopping one action to do another.
Fed up - 참다 못해 화를 냈어요 (couldnt take it anymore and got angry)
Breaking point - Reaching limit of tolerance
Transition - From enduring to acting
See examples below for varied real-world usage.
Often with 참다, 기다리다
Leads to reactive action
Unable to take it anymore, I shouted.
I couldn't wait any longer and went in first.
I'm beyond hungry to the point that it actually hurts.
I couldn't stand watching his rude behavior anymore, so I said something.
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