Ok, we were through allllll of this a couple months ago, but to summarize two important points not yet mentioned here:
1) line breeding is not uncommon in plenty o' other domestic animals besides chickens.
2) A parent and offspring are EXACTLY as related as a brother and sister are. That is, parent-offspring mating is exactly as "inbreeding-y" as brother-sister mating.
It is true that parent-offspring matings are used much more often (in ANY domestic animal breeding programs, not just poultry) than brother-sister, but not because of a difference in inbreeding coefficient. The usual reason is simply that you know (well ok, can make a much more astute informed guess about) what genes a parent carries than a sibling, simply because the parent has been around longer, reached full maturity, and often been progeny-tested in previous matings. Whereas a sibling you're less likely to have a good idea what genetics its carrying.
But, repeat, parent-offpsring matings are *exactly* the same degree of inbreeding as brother-sister.
The more you outcross, the harder it is to accentuate and 'perfect' the traits you want, but the less likely you are to get individuals displaying really defective traits.
The more you linebreed rather than outcross, the more you accentuate ALL traits, both good and bad -- which means more significantly-not-what-you-wanted individuals to be culled, but OTOH forcing recessive traits to 'surface' allows you to cull out carriers of those alleles and thus have some possibility of eliminating them from your population altogether.
At *some* point you tend to need some outside blood -- preferably not too outside, like from a closely related line -- as fertility begins to drop or recessive problems that you can't conveniently cull out begin to surface. But that may not be for some generations, and doesn't necessarily require *much* fresh blood to correct.
Pat