*For the purposes of this bog, I am including linebreeding under the title of "inbreeding", but there are some differences. Inbreeding refers primarily to the breeding of close relatives, such as offspring to parent or sibling to sibling. Linebreeding refers primarily to the breeding of more distantly related animals, such as two animals who have the same relative 3 generations back in their pedigree.*
Inbreeding in and of itself is not bad or good. Inbreeding does not cause genetic issues, as is popularly (and incorrectly) believed. Inbreeding may be good or may be bad for a breeding program, depending on how it is employed.
In a nutshell, inbreeding concentrates the genes that are *already* present in a bloodline, it does NOT create new genes, it does NOT cause genes to mutate, it does NOT cause genetic issues. Some of these genes present in a line are going to be desirable, some may be less desirable, some may be outright undesirable. The breeder doesn't know which genes will be expressed in the offspring, and this applies both to outcrossing (breeding unrelated animals) and inbreeding. But this is also why inbreeding is such a valuable tool in the breeding program. By concentrating those genes, a breeder can now see what traits are actually present in the line by bringing those traits to the surface. Once the breeder knows what traits are there, the breeder can work on selecting or eliminating those traits.
When a breeder always outcrosses, those genes (both desired and undesired) are going to be there, but may be passed on unexpressed for generations, passed on to more and more animals, spread to other bloodlines. When the genes finally match up and are expressed, the breeder now has no idea how common those genes are in the line, where they came from, or how to eliminate them. For all the breeder knows, every animal in the breeding program may be a carrier of those undesirable genes!
By inbreeding, a breeder is able to "magnify" the traits already present in the bloodline. If those traits are undesirable, the breeder can bring them to the surface (rather than passing them on and spreading them unexpressed for generations) and work to eliminate them. Likewise a breeder can use inbreeding/linebreeding to select for desirable traits (such as good health or temperament).
Using a fairly innocuous trait as an example... a breeder may be breeding black rats, but unbeknownst to that breeder these rats carry the gene for blue. The breeder breeds unrelated rats together and doesn't get any blue rats, so the breeder doesn't know those rats carry blue and are spreading the blue gene around. Finally the breeder tries a sibling pairing. Lo and behold, blue rats in the litter, since both parents were carriers of the previously unexpressed blue gene! The breeder doesn't want blue, it is an undesirable trait in this breeding program. Now the breeder knows there is blue in the line, the breeder can work to eliminate it. Any blue babies in that litter will be eliminated (i.e. pet placed) from the breeding program. The black babies may be bred together, or bred to another relative. Through this careful selection, the breeder can systematically eliminate the blue gene from the breeding program and bloodline. When the breeder brings in additional unrelated rats to supplement the program, the breeder will know to carefully research the line to make sure it is free of blue, or else risk having to eliminate the trait again.
This elimination of blue (or other undesired trait) from this breeding program will take time, and lots of careful planning, but it is the best and easiest way to eliminate the undesired trait. Otherwise that trait can be carried for many generations. For example, I have had beige show up in litters many many generations after the last beige rat showed up in the pedigree. This shows how long some traits can be carried unexpressed. Every trait that is carried can be spread throughout a bloodline.
Now color is a pretty harmless and simple trait. Most colors do not cause health problems, so really color is negligible in a breeding program when it comes to the most important matters (health and temperament). But this simple example shows how inbreeding can be so important to eliminating (or selecting for) certain traits. Imagine now a trait that is control not by one simple recessive gene, but by multiple genes that may be partially or incompletely dominant! Most traits in an animal, especially health, are NOT controlled by single, simple genes, but by multiple genes that may not be simply recessive or dominant. These genes may be incompletely or partially dominant, they may be epistatic, sex-linked or sex-influenced, controlled by environment, etc etc. There are so many more variables to consider. This is not only what makes a good breeding program such a challenge, but also why inbreeding should NOT be seen as a red flag, but actually as a valuable tool when used properly and logically. Inbreeding is one the qiuckest ways to isolated and eliminate the undesirable traits (such as health problems) in a bloodline. It is true some animals will be born with undesired health problems, but without this carefully planned inbreeding, such traits can, and likely will, be spread throughout a bloodline, making isolation and elimination nearly impossible, and dooming many more animals to those problems.