Last year, my next-door neighbor told me that she never grows eggplants because we don’t have enough days in our growing season for them.
A few weeks later, a neighbor a few streets down gave me a spare eggplant she’d just grown from her garden.
Yep, they definitely don’t grow here!
(Laugh.)
What have you grown in your area that you’ve been told was impossible?
It’s pretty much my MO to grow everything that shouldn’t grow well here, atleast outdoors. Some just out my own interest like melons, watermelons, sweet potatoes and peppers although I was aware that I should grow them in a greenhouse. I did grow also in greenhouse at first, but also experimented outdoors. And failed. Mainly for lack of skills, but that didn’t stop me from trying and eventually figuring out how to have best changes of success. Moschata and eggplants I included more recently. I think I had one or two failed tries with moschata, but then I kept hearing comments like “you can’t grow them outdoors” or " they need alot of heat" etc so ofcourse I had to try. I really didn’t need to as other speccies of pumpkin grow better so it was just for the challenge. Same with eggplants. Never really even had them before and was very suspicious about eating them, but I noticed this year that I even liked them so all the more reason to grow them. This year I did learn that oca and mashua dont grow here, or more specifically, dont produce crop here. Not yet anyhow. Daylenght sensitivity is something that is quite hard to overcome and our season is just way too short that they would experience any short days. Ocas especially had great vegetative growth that if someday there are daylenght neutral varieties they would do great here. Dont think it’s impossible as that’s how potatoes were before they arrived to Europe and it only took little more than a century before it spread throughout the continent. But at the moment it’s not something I spend time on.
Nothing so far 
. This is exactly what I’m hoping to do with the benign neglect and let-it-be attitude towards outcome common to landracing and STUN.
I’ve grown food crops in my yard if that counts, where they are dry-farmed up to or through final harvests and many of them are vulnerable to being peed on and charged through by dogs. Our cowpeas and some of our squash had to be pretty tough to deal with that.
An oft-repeated litany of last growing season: “{Dog name}! No pee on Dadder’s crops! 
”.
We’ll be growing even more food outside the formal garden this year - - some dog-proof, much not. We’ll see about crops self-selecting for nitrogen burn tolerance or recovery, or maybe have a trap crop patch that’s irresistible to pee on? Do dogs like peeing on banana trees? 
Now that I think about I think my wife may have actually told me I wouldn’t be able to grow food crops in the yard. I said “I can as long as I’m okay with them being peed on and destroyed.” Challenge accepted! (I do have an emerging game plan for next year’s iteration but that’s another story)
I was told pistachios wouldn’t grow at my old place. And sweet potatoes. But more common was the look of shock and “That will grow here?” when I told people what I was growing.
My sister grew lemon grass beside (not inside) her little greenhouse. Other than tropicals (lemon trees and avocados, which I mostly keep inside) I just assume they will grow until they prove otherwise.
Oh, smart! Yes, I can easily see something outside a greenhouse getting a tiny bit of extra cold protection by the proximity. And it’s definitely worth using any heat that escapes, rather than letting it just dissipate. Plus any crops outside the greenhouse probably act as a tiny bit of insulation to keep as much heat as possible in!
Hee hee. I like your attitude. It makes sense to give everything a try! And that goes double for when you already have the seeds.