I'm not sure what I despise. Despise to the point of "I eat it I puke". Despise to the point of being held at gun point. "Eat this, or I'll shoot you!" And I'd say: "You might as well shoot now, and we'll get it over with!"
I hated milk when I was a child. But it's been years since I went near the stuff; no idea how I'd react. I can stand froth on cappuccino, but not wild about it. Also the type of milk might make a difference. I had raw milk once as a child--despite all the whining out there about how "dangerous" it is--and it was much better than the crap usually poured into my glass.
Canned tuna is another thing I hated, and it seems to me it made me gag more than once. I was forced (well not forced, but felt obligated under circumstances) to have something with tuna a year or so back, and managed to choke it down. I didn't precisely gag, but it was not pleasant. On the other hand, I'd be willing to try fresh tuna--someone told me that fresh tuna is much different.
I'm not into meat in general. After a certain point, my family never really had much meat that was just cooked meat. To save money, my mother bought cheap stuff, that got cooked as part of something else. So...I have little real interest in a thick steak. (But don't necessarily despise it, and would be curious to try 100% grass fed, locally produced steak.)
I'm not much into seafood. I will eat fish, although not often due to price. A lot of fish I don't like, but that might be preparation. I have no real interest to try sushi. Clams I eat only in chowder; no interest in trying them otherwise. No interest in oysters.
Processed meats are another thing I mostly am happy doing without. At one point, we were caring for my grandmother, who just loved that crap. We cooked it sometimes to make her happy. I hated mainstream sausages--no taste, all grease. I privately called one common brand "Greaseshire Farms." And ring of bologna I strongly disliked, but could choke down if covered with something. And I'll be happy to avoid Spam, too.
I suppose a lot of vegetables could come under fire, but it would be more about a specific preparation. Like mentioned above, I hate canned peas. Frankly, I wonder why we even continue making them. Frozen peas are so much better. I don't like overcooked vegetables, either.
And then I really don't like standard cheap bread. I don't quite despise it, but it's another thing I'd be happy to never eat again.
