Interesting question, Chris! Substitute the word "writer" for any other type of work and, for me, the short answer would still be "yes."
No doubt becoming a professional writer is not for everyone. It takes a tremendous amount of discipline, stamina, and practice to become a good writer. Like many of the creative arts, writing is subject to significant criticism; however, it is imperative to not take the criticism as a personal attack. Instead, it should be received as an opportunity for growth and development as a writer. Therefore, if there are folks who are critical of your interest in becoming a writer, it may be worth taking the time to find out why they are challenging your decision. For example, maybe the challenge is that financial success may be hard to come by as a writer. It's a reasonable criticism; so, maybe you don't quit your day job so you can pay your bills and eat but you still write. Still, there may be others who have no reasonable criticism to articulate; I call them the "naysayers." Unfortunately, there are people who are unhappy with their own lives and express jealousy by discouraging others from dreaming big. Ignore them.
No one can dictate the course of your life nor should you give them permission to do so. Everyone should follow their passion and cultivate their talents. After all, it's your life. Limit the discouragers in your life and be true to who you are; then you will find more peace, happiness, and success in your life. Embrace your talent, skills, and abilities as a demonstration to the world of the beautiful individual that you are.