It's fine to linebreed so long as you really know the breeding stock you're working with. It's an issue when a serious flaw is overlooked for the sake of all the good things, such as HYPP in Quarter Horses, and many of the canine issues, and any other species. You need to have genetically diverse and healthy animals to start with before close breeding like that. Adding outside blood every couple of generations.
It without a doubt sets a type, some very noticeable and desirable traits. It's the making of a bloodline, that will prove to be reliable and predictable. It's also used in the formation of new breeds or colors, to make those new traits reliable and predictable.
With chickens not commonly used as "stud" animals, if a flaw in the genetics is found, it hasn't been spread all over the bloodlines of others like with dogs and horses. That's where problems arise within an entire breed, is when one fabulous stud is bred again and again, passing on everything he has, good and bad. It can go unnoticed or ignored for generations. Anyone that "outcrossed" to him to in theory improve their own lines, potentially added a very serious genetic illness, initially not even knowing it until years later and countless animals created.
Culling is the most important part of it, knowing which animals to remove and why. Line breeding willy-nilly without goals is pointless. You only do it if you know what you're looking for. If there is a type you're aiming for, or a new color for a breed, then you need to know who to cull and who to breed back to based on what they produced. You have to make A LOT of babies because there will be A LOT of culls starting out. It can take 4 generations or many more to produce something that will be reliable when bred to another of the same type. Depends on the culling through out the whole process.