Since I never set out to be a writer, this question requires a little pondering. I never walked around announcing to my family, "I'm going to be a writer someday!" (insert little baby voice). In fact, until well after my first year of college, I told everyone I was going to go into that other profession that strikes fear in parental hearts: acting. Right, acting. I might as well have said I was going to make my living creating gerbil homes of out of shoelaces. But however worried my parents were, they never, ever let on. All they did was nod and smile and wave me cheerfully off to college, knowing that about two seconds after entering my first intro to acting class, I'd realize that 90 % of the people there were better actors than I was. And that's exactly what happened. But when I did eventually get around to telling them I was going to write full time (this was about seven years ago, when I was twenty-five), they also did not say one negative thing.
I'm not answering this question very clearly, I realize, but what I'm trying to say is that I think I could have been easily convinced NOT to be a writer, but because my parents (and my husband) never, ever tried to talk me out if, not even once, I just went ahead and did it. And it's worked out okay.