There are a lot of misconceptions about inbreeding/line breeding. In the world of chickens the father/daughter mating is quite common. Because it is easier to buy a good cockerel then breeding back to such a bird is a way of upgrading ones own stock. In genetic terms mother/son is equally good if the hen is a good example of her breed/variety. Either way it is only worth doing if the bird is a top class example.
It is unlikely that any negative consequences would arise but if it was done repeatedly then inbreeding depression may give rise to impared productivity, size, disease resistance etc.
In the world of poultry brother/sister matings are rarely done. This may be more due to custom and practise. I am planning a half brother/sister mating next year (same father, different mothers).
Close breeding is a way of fixing type and developing a strain. If practised for a number of years then variation is reduced and greater uniformity is found in ones hatchlings.
Poultry, sanity in a mad world!
Sheep, insanity in a rational world!