The problem you're running into here, is that the rules are ambiguous:
The square you start out in is not considered threatened by any opponent you can see, and therefore visible enemies do not get attacks of opportunity against you when you move from that square.
These rules are written for medium creatures, and don't make a lot of sense when applied to a large creature (which square is "the square?"). There are three basic interpretations:
All four of the squares occupied by the large creature become non-threatened for the duration of its move.
The squares left by the large creature during its first "step" of movement are non-threatened.
The large creature must designate a single square within its space to be non-threatened.
The third option is a bit of a stretch, and can probably be eliminated. It fixates heavily on the singular square wording of the original, but adds a lot that just isn't in the rules to preserve that. It also renders Withdraw more or less useless for large creatures.
Of the remaining two, the first is closest to the original wording. The squares you start in aren't threatened; everything else is. This gets a bit weird in practice, because a medium creature is unlikely to ever withdraw back into the square it left, whereas large creatures do this all the time.
Finally, the second option probably comes closest to the "feel" of the original withdraw rules. You get one "square" of movement free of opportunity attacks, and everything else provokes. This interpretation also means that large creatures have the same problem with an adjacent 10' reach that medium creatures do.
Were I running a game, I would probably use the second option: The squares left by the large creature during its first "step" of movement are non-threatened.
That's just what feels natural to me. But your mileage may vary.