Each year, I give up several things for Lent. Always alcohol and sweet things. In the last couple of years, caffeine as well (the headache only lasts for the first 72 hours).
But "giving up" has many senses, and is one of those confusing multiple meaning phrases. To give up, to relinquish, to surrender something (to someone or something else), is one meaning. We may "give up" cigarettes. Or be exhorted to "give it up" for the headline act, applauding and cheering in a stadium.
Or we may just "give up" in the sense of admitting defeat. In the last few weeks I've seen a few people say they are giving up looking for an academic job. This is not a temporary forbearance, like my giving up alcohol. They have made a decision to draw a line under it and move on. In the humanities, I've seen a number of people make that decision over the years. But in so many cases it was not a decision they made, so much as one the market made for them. They were perhaps not the giver-up, but the sacrifice that was given up by greater forces.
Each Lent when I refuse a glass of wine or a cocktail, someone will try to force one on me - often with some comment like "God won't mind" or "you can cheat a bit". I'm always puzzled (and sometimes annoyed) - nobody is forcing me to do this. I want, for myself, to give things up. Nobody else is policing it. So I don't understand why people think I'd be looking for loopholes on my own goals.