anger, breathlessness
愾 centers on a strong internal state that disrupts normal calm: anger that surges up, or breathlessness that leaves one gasping. Both senses share the idea of an intense, agitated inner condition.
愾 combines the heart radical 忄 with 氣, which likely contributes both sound and the idea of breath or vital energy. The character may have originally expressed a surge of emotion or breathlessness tied to the heart and qi.
The heart radical 忄 beside 氣 (breath/energy) suggests a heart overwhelmed by rising energy: either anger boiling up or breath caught in the chest.
For ガイ, imagine a guy so angry he can't breathe: guy -> ガイ, and his heart 忄 is pounding with 氣.
hostility; enmity