It all depends on the context. Parents are human and say things often they don't really mean, If the day had gone really bad and there were teen issues going on, I can see me saying it from time to time, A parent oftens just wants to give up and walk away, it does not mean they will or do, but I doubt any parent of a teen did not want give up on a child.
I had one son for sure that I wanted to give up on a dozen or more times, never did but sure wanted to.
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