Part of the misunderstandings come from differences in the way the terms are used within the scientific/medical field, and how it is commonly used by breeders. These are the most commonly accepted definitions used by serious dog breeders and will be the definitions used within this article. 

In-breeding - This is the breeding of closely related animals. Brother/Sister, Parent/Offspring.

Linebreeding - This is the breeding of animals that share common ancestors but are not as closely related. For example uncle/niece and half sibling matings.  Typically, breeders linebreed off a particular animal.

Out-cross - This is generally considered the breeding of animals with no common ancestors within the first 4 or 5 generations.

 Common Misconceptions

Linebreeding causes genetic diseases - Breeding closely related animals increases the possibility that any bad genes in a line will show up. It does not 'cause' genetic disease.  If those genetic diseases exist in the dogs, then linebreeding will express them earlier rather than later (as with Outcrossing).

Out-crossed dogs are healthier - This is only partly true. There is a known phenomenon called Hybrid Vigor. Two animals of unrelated strains breed and the offspring is often bigger and grows faster than it's purebred cousins. This method is often used by farmers in order to get their animals to market sooner. But one of the biggest misconceptions of hybrid vigor is that it applies to all animals of mixed heritage. Hybrid Vigor only applies to the animals that are the direct offspring of the crossing of the unrelated strains. In other words if you continue to breed animals of different strains there generally will not be any additional increase in hybrid vigor. If the unrelated strains share common genes for genetic disorders, hybrid vigor will not over ride the risk of the disorder showing up. Out-crossing can also cause problems if widely divergent physical types are mixed due to differences in growth rates and bone and muscle sizes.

 Benefits Of Linebreeding

By definition, purebred dogs have a smaller gene pool to draw on than mixed breed dogs. That smaller gene pool gives the breed its individual characteristics, such as physical appearance and temperament. It is what makes a poodle a Poodle and a Golden Retriever a Golden Retriever. But there is considerable controversy with regard to whether the gene pools of the modern pure-bred have become too small.

Linebreeding is more likely to help "set" or "fix" a particular trait within a breed or a line by narrowing the gene pool to favor those traits. So if a breeder is looking to set a particular desirable feature of their line then linebreeding and choosing the offspring most strongly possessing that trait can be beneficial.

Linebreeding can also help identify those bad genes that exist within a line. Dogs possessing the bad genes can be eliminated from a breeding program and carriers also identified.

To use this method responsibly a breeder would not want to linebreed off animals with known genetic disorders, temperaments not in keeping with it's given breed, or known serious structural faults, or to in-breed frequently even on healthy-superior specimens.

Line-breeding over successive generations will result in less variations of physical appearance outcrossing, and when done properly carries fewer long term risks.

According to geneticists. Line-breeding can be carried on for many many generations without deleterious effects on the line or breed as long as the individuals involved have few hidden genetic disorders.

 Outcrossing

Outcrossing in terms of pure-bred dogs is the breeding of unrelated dogs. On a pedigree no names will be repeated within the first 5 generations.

This type of breeding has both advantages and disadvantages. Which as it turns out are flip sides of the same argument. With outcrossing you are maintaining the greatest genetic diversity, but this also leads to the least consistency in terms of physical appearance and other traits.  Outcrossing does not guarantee that the animals won't develop genetic disorders.