How can you write such a good letter in English but not be able to speak it?

Literal

This-much skillfully English [by-で] letter [object-を] can-write [despite-のに] why cannot-speak [explanatory-の]?

Built around ~のに ('even though,' 'despite'), which links a surprising or contradictory pair of facts — the kind of 'but' that carries a note of frustration or incredulity. こんなに ('this much,' 'to this degree') intensifies 上手に; together they make the incongruity sharper ('this well, and yet...?'). The particle で on 英語で is the instrumental 'by means of English,' and 書ける is the potential form of 書く. Note that 話せない contrasts with 書ける via the same ability frame — 'can write... but can't speak.' The casual の? ending turns it into a rhetorical question with a tone of surprise.