Dual-purpose guns designed for the wrong attack geometry

Why were interwar British cruiser and destroyer guns inadequate at high-angle anti-aircraft fire?

They were designed around aircraft attacking nearby capital ships, not the escort itself, so the assumed engagement geometry understated the required elevation.

British designers expected cruiser and destroyer guns to engage aircraft attacking nearby capital ships. From the escort's position, an aircraft over another vessel could remain at a relatively low elevation, making limited high-angle performance appear acceptable. An aircraft attacking the escort itself would pass rapidly overhead and demand much greater elevation. The guns therefore embodied a faulty threat model, illustrating how technically competent engineering can still produce an inadequate weapon when the assumed engagement geometry is wrong.