Was pondering backstories.
Now, other classes require training, too, and some fully as specific as a thief's -- a wizard, or a cleric -- but it's a lot easier to see paths from a lot of backgrounds there. Any church might be interested in a pious and gifted child, and a wizard might take on a pupil from a lot of backgrounds (even, out of kindness, an urchin).
There are various backgrounds where you might be taught thief skills. Picking pockets could be learned by an entertainer as a side effect of sleight of hand. A locksmith could pick locks. Sneaking (about and attacks) could be useful as a merchant in a caravan. . . .
But it's hard to see how someone could acquire all the skills from most backgrounds. Street urchin, thief family, other criminals, yes, but that is kind of limiting.