Maybe you haven't thought about it before now, maybe you have, but the idea of career = identity is long rooted in history. It's about as synonymous as breathing = needing air. We've been defined by what we do. Even back to cave and prehistoric times = Men hunt. Women gather. Men fight. Women raise families. I'm sure there were men who gathered and women who hunted, but the exceptions aside, you can follow that idea of Person = Job throughout history. Gladiators fought. Soldiers fought. Oracles say the beyond. Healers healed. Medicine wo/men healed. Teachers taught. Blacksmiths forged. Cooks cooked. And on and on and on.
And if you look at that long enough you realize people were essentially raised into a (one) specific career (unless they were conquered and forced into another, but even then it was still basically ONE area of focus). And humans died young. Living to or beyond 50 was not the norm (why we have midlife crises early and not at 50). Even the concept of last names stemmed from the idea of being derived based on WHAT you did (smith = blacksmiths; housers = worked in the house; cooks = cooked) or WHERE you were from (Saxon, etc). https://www.english-heritage.org.uk/visit/inspire-me/blog/blog-posts/norman-saxon-surname/
So all this to say, the idea that today's attempt to break free from your career as your sole identity, having to get permission from one career to partake in another, etc., may seem annoying or even blasphemous, but, in reality, it's one of the most historically-based things we have. I don't think it's right anymore. I think humans and the human spirit is changing at a pace quicker than we can emotionally or social evolve, but I am not surprised it's hard to separate one from the other.