What does “give up on” mean?

to stop hoping or believing that sb will change, get better, etc.

How is “give up on” used?

In American Beauty (1999), one line is: “Thank you for trying to teach me. Don't give up on me, Dad.”

The clip at the top of this page is from American Beauty (1999).

Thank you for trying to teach me. Don't give up on me, Dad.

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