In the US, grain production (and actually farming in general) is highly subsidized, such that you can’t infer much about the cost of growing food from the prices you pay for it.
I don’t know where you are, but the answer is probably local to you.
But in some countries, fresh fruits and vegetables are considered a luxury item. It is especially apparent in Japan, where you are only able to buy top quality vegetables with a flawless appearance and a matching price. Everything else goes to the food processing industry.
* People are willing to pay x for a pepper
* People do not consume significantly more peppers if the price is lowered
* People are willing to pay y for a kg of chicken
* People buy significantly less chicken if the price goes up much higher
TL;DR it's about price vs volume vs profit margins, and I'm sure they continuously hover around an optimum for these products.
In any case what you say isn't even true: At my local supermarket cucumbers are £1.80/kg, while chicken starts at £1.95/kg for super-cheap chicken thighs with bone-in, up to nearly £20/kg ("Sainsbury's Norfolk Black Corn Fed Free Range Chicken Fillets" in case you want to know), the average being around £5/kg. There are no pork products at all below £4/kg.
As somebody who's also from the central EU, it feels like you are low-balling that price there. You would have to look really hard to find chicken breast as such a low kg price because the average is more like 5 €/kg usually higher [0].
Personally I wouldn't even buy such cheap poultry because with a price like that you can be very certain these animals must be farmed in rather "optimized" conditions. Just like with eggs or milk, these are items I'm willing to spend a bit of extra money to support better and more humane practices.
Trying to do the same with meat is very expensive, did it recently ordering turkey breast, ended up paying 8€ for 400g, thus I reserve it for special occasions.
In that context, your comparison between peppers and chicken breasts is also not that good. Peppers are a very bad vegetable source of proteins, to replace chicken breast one would eat something protein-rich, like beans and those happen to be dirt cheap pretty much everywhere, particularly when buying them in bulk and dried.
[0] https://www.supermarktcheck.de/sb-haehnchenbrustfilet-frisch...