Dudley's birthday — how could he have forgotten? (original English version)
The nuance of the English version is that he did forget the birthday, but based on some previous experience (in this case, unpleasantness) it seems unlikely that he would have forgotten and he feels foolish for forgetting.
I'm struggling with the Japanese meaning, In particular, why the volitional form? My literal translation would be "How would he be able to forget?", suggesting that he wants to forget but cannot (I'm assuming this is potential rather than passive. That's not clear to me either).
In summary, what is the actual nuance behind the Japanese sentence and how does that arise from the grammar?