Giving up has some different connotations. We give up things we want to get something else. We give things up that aren’t great for us for Lent. We give up and are derided for being quitters, by others or by ourselves.
In this passage Jesus asks us to give things up and to take things up. Give up our lives or give up the world? Keep ourselves or take up the cross? By the end of the passage, Peter and James and John have to decide if they can give up the idea that Jesus is anything less than the Messiah, the Son of God.
That is something we have to decide as well. After encountering Jesus, is he just a wide Jewish man, or is he the Messiah? Is he our Savior and Lord? And if he is, what else do we have to give up and take up?