On Breeding Better Dogs

Ok y'all talk about line breeding a family of dogs vs scatter bred. My question is how is line breeding essentially any different than getting say 6 dogs on my yard (none being related in any way and most of them being crossed up mutts) that I sure enough like and think are worthy of breeding, breed them, and start a "family" of dogs and start line breeding from there. Seems like most of you guys are dead set on pure bred dogs. But the few old timers I've had the pleasure of talking with will tell you. Way back when, you bred best to best. They didn't care if it was a black lab/ pug mix. If it hunted good it got bred. Seems to me a good dog will produce good pups. 2 good dogs should breed a higher percentage of good pups. But I'm not sure how breeding a gyp to her dads litter mate brother raises your odds. Or why people have converted to that method when scatter bred best to best dogs worked for people for a long time