What if white plays 2 at 3? After black playing at 2, white can go under?

Black can push through and clamp, preventing w from intruding into his area which fulfils the stated goal of the problem. As to why white might prefer to simply push, there are still weaknesses left in this position, like maybe later white can cut, or maybe white can clamp. Just playing the problem as it is in the diagram leaves some aji, basically.

Ok, thanks, Chariot.