And also to Cajun (but I don't know how to quote two people.)
Good answers. (From what I have gathered so far in arming myself with knowledge so I can begin breeding Bettas within the next year.)
The IBC tries to stress starting out with a quality pair of fish is really important, as do many other breeders, and clubs internationally. All these fish have been line bred, and inbred, to some point. (Brother to sister, father to daughter, and any combination in between like indjo said above.)
In the research I have been doing, a brother/sister pair of fish is a good way to start your breeding program if you want to more closely duplicate the traits of the parent fish. Line breeding sets good and bad traits into your stock. When you outcross to another fish, from another line, you introduce all the traits from that line into your own. Most likely the other line of fish has their good and bad traits well set into their stock because that person was working on setting in traits they were working on.
You then take the offspring of this union and line breed to hopefully set whatever trait you wanted to improve, and remove newly introduced bad traits.
Inbreeding to some point is needed, as is careful outcrossing. Having a clear vision of what you are wanting to achieve in your fish, and to stay focused on that goal, is really important.
You have to be careful selecting fish to outcross to because in some cases you can introduce traits you don't want into your line and it may take years to get the undesired traits out again.
For example: If you are breeding solid color fish and you introduce marble it will take a lot of generations, to get out of your fish if you introduce it, and don't want it.
(I could be wrong on the example. I am going from memory off stuff I read, but I think marble is one of the hard-to-get-rid-of traits.)
In a nutshell it's why everyone says start breeding with quality fish from breeders. If you talk to breeders you can often get some background on the fish you are wanting to purchase.
I hope I'm not way off base here, but as they said it's either safe to breed up to gen 6 or 8. I can't remember if it's the rule of 7's or the rule of 9's.. I can't find info on it anymore, and I didn't seem to have bookmarked it.
But at one of those numbers 7th or 9th generation, you outcross no matter what. If anyone can link the rule to me I would love you so I can bookmark it.
Sorry this was long winded!
Best Wishes