pedigrees?

I've seen some things for a while saying low generation horses are ideal. Is there a reason for this? Because I have some horses that I think are reasonably nice (I may be wrong feel free to look) that have pretty full pedigrees, some of them don't even show foundation lines unless you click on a different horse on the pedigree... just curious 

It's not how short a pedigree is that a breeder is concerned about; it's how clean it is. I.e. no inbreeding, no repeated ancestors, like several of the horses in a horse's pedigree heads back to the same sire or dam, and how many foals each sire and dam had. 

Many players, including myself, prefer to breed their horse's 1-4 times, less if possible, work hard with their horses to get them to as high of stats they possibly can be, and then breed them; you can have some amazing foals. :)