To not give a damn means to not be interested in or worried about someone or something.
Not care about; be indifferent to.
1. Most companies don’t give a damn about the environment.
2. I don’t give a damn if she talks about me behind my back.
3. The movie was so boring that I didn’t give a damn about what the rest was about.
4. If you don’t give a damn about how I feel, stop asking me in the first place.
callous, cold, could care less, emotionless, indifferent, laid-back, passive, unconcerned, uninterested, uninvolved