There are key differences between "giving up", and "letting go". For example:
Pros for giving up: Sometimes, it is best to give up, such as if you are having a hard time climbing Mt. Everest, which, in this case, may result in death if you do not admit your limit and go back down.
Cons for letting go: For example, if you are hiking with your love one, and she slips off the trail and about to fall down, and you catch her, you wouldn't want to let go, because:
1) It is a human's life at stake
2) She holds a special place in your heart, and you do not want to see her demise.
And so you continue to hold her.
Another example for giving up, can be when you send an army against the enemy. If there fortifications is too strong, it would be better to go around rather than go directly against, for you are trying to reach the same objective with less casualty, then gain glory
hope this helps
