oppose, disobey
乖 centers on going against what is expected or commanded: opposing, disobeying, or deviating from a standard.
乖 is thought to combine 北 (back-to-back, opposing) with a phonetic element, reinforcing the idea of divergence or opposition. The exact historical development is uncertain.
The top looks like a person turning away, and the lower parts suggest two separate paths. Picture someone deliberately walking the opposite way to oppose or disobey.
For カイ, imagine a defiant kite flying against the wind: kite -> カイ, and the kite opposes the breeze just as 乖 means to oppose.