People will often define themselves by what they do, this has been true since the stone age when people named themselves after their profession. The more things you do, the less impact there is on your opinion of yourself if someone says that one of the things you do is substandard.
Having hobbies will help avoid the trap that people get into when they take a job "because it pays well" and not because they are interested in it. The trap is sprung because it is harder to work at a job you're not invested in, and you don't generally do as well as people who are invested. So you can end up taking time away from other fulfilling activities to get told your doing badly at the thing you are spending all your time trying to do. That is a horrible place to be mentally.