I can not stand mushy vegetables. I despise mayonnaise. I don't like artichokes or eggplant. I don't like candied yams/sweet potatoes (do you REALLY need all that sugar in and all those marshmallows on top of sweet potatoes?!? Gag!).
Mushy vegetables, eggplant, and artichokes taste godawful to me. Mayo makes me want to vomit. Candied sweet potatoes make me want to vomit. I'd much rather have plain sweet potatoes with a little salt.
So, I avoid pasta and potato salads, anything with artichokes or eggplant in them, and veggies that are mushy. I also prefer plain salads (lettuce, green onion, spinach, other greens) to salads that have lots of other things in them, like tomatoes, strawberries, etc., and I prefer vinaigrette or no dressing at all to ranch, French, or any number of other salad dressings. I like tomatoes and strawberries and other things, but not in a dressed salad.
I also don't like barbecue sauce. If you barbecue or grill something and need to put sauce on it to make it taste good, you're doing it wrong, IMNSHO.
Yes, I'm picky. However, I don't let my pickiness ruin meals for other people. There is rarely a meal where NOTHING that is on offer is something I am willing to eat. If there is a salad, and it is undressed, I can eat around the ingredients I don't like. If there is barbecue, I order it dry if I'm out, and none of my friends or family sauce it before service, either, because some people like different sauces. On only one occasion per year do I encounter the main meat dish already sauced, and I just don't eat it (after having tried it several times and continuing to dislike it), and bring my own lunch that day (it's at a regional shooting match, where the paid entry also buys you lunch for that day).
If there is truly nothing I am willing to eat, I wait until later, or go get something I am willing to eat. The only time that is not possible is when I'm out in the middle of nowhere (like at a match) and have forgotten to take something with me. Unfortunately, unless I'm the one doing the cooking, at least one place I visit for several days at a time, I get no veggies, because the person doing the cooking there really seems to like to cook the snot out of veggies, and I never manage to catch her to dish some out when I think they're done before she cooks the crap out of them. So I eat a token few to be polite, wash them down with whatever else has been served, and deal.
My parents did the sit-at-the-table thing with me with several foods. The one I remember most was raw tomatoes. I could not get them down without vomiting because of the blandness and texture. It took me YEARS after I reached adulthood to even consider trying them again because of that experience. I will eat raw tomatoes, now, but still have issues with their texture, at times.