What exactly is the argument against eggs again?
Hens, ducks, etc. will lay an egg most every day, sometimes skipping a day or two. They will be protective of the egg for maybe an hour and then abandon it. Farm birds don't go into "heat," but they do get "broody," which is where they get the desire to incubate a clutch of eggs. Female birds can get broody even if there is no male around, so they can try to incubate a clutch of not-fertilized eggs. If a bird is not broody, they will not try to hatch the egg, whether they have mated with a male or not. Eggs are nutritious by themselves, can be used for all types of cooking, and can even be used in medicine and healthcare in general. If the bird doesn't want their egg, why waste it? Oh, and unless the egg is incubated, the egg won't begin to form a chick. If a hen lays a fertilized egg but doesn't incubate it, it's just a fertilized egg and not a baby. In mammals, the embryo begins to form within a day of conception, give or take. Birds aren't mammals. If we eat an egg, it's not like we're eating newborn kittens.
Also, over time chickens will actually eat their own eggs if left there (and it is actually good for them, feeding them eggshells makes their own eggshells stronger) and they will also cannibalize dead chickens. They have also been known to eat another chicken directly after killing it during an attack.