What is the logical conclusion? How far do you take it? Should I, say, not be proud of my children's accomplishments? After all, I didn't do them, they did. I'm a musician and play in bands. Should I not be proud of things my band has accomplished? What my band does is stuff that I can't do alone, and they can't do without me.
Obsessively focusing on the individual and rejecting one's role in society is nihilistic and alienating. If you gotta do it, I suppose you do you, but please don't drag me into your sad, lonely world. I'm going to enjoy my place in my family, my town, my country, etc.