User blog comment:JohnnyN64/Mysteries of Fairy Tail/@comment-6152051-20140611062120/@comment-7418318-20140611155550

I can see three reasons:
 * 1) Parents wouldn't allow their children to roam around in the wildernes alone, so none-orphans wouldn't have gotten into situations in which the Dragons could find and adopt them.
 * 2) The Dragons intentionally chose orphans, because they didn't want to rip children out of intact families.
 * 3) They chose orphans because nobody would come looking for them. If the children still had families, those families would surely come after their children. Not something you'd want when you're hiding from civilization.

But that's assuming that the Dragons really chose orphans. With the total lack of information about the DS's pasts there are other possibilities too.

The children might have been given to the Dragons willingly by their parents (maybe some kind of cult?) or the Dragons could even have killed their families. Since they are trying to save the world from Zeref, such a sacrifice might thought as necessary for the greater good.