I agree with this. I've read somewhere (source needed) that it takes babies about 10-15 tastings to get to grips with a new, unfamiliar flavour, and I'd imagine the same principle applies for adults.

More anecdotally, both my father and my OH started off really strongly disliking the flavour of coriander in their teens, then grew to really like it after they've tasted it in a variety of contexts. My father also had this with yoghurt, and I myself with goats' cheese.

In fact, I'd suggest you start with more variety than just one vegetable, since if you attack on all bases simultaneously, statistically speaking you're going to start liking one of them faster!#

Edit: only source for my claim that I could find which cites a study is here. The study also suggests that babies learn to like a food faster if it comes paired with something they already like, which gives evidence to some the other suggestions mentioned.