insert between
夾 centers on the idea of being inserted or wedged between two things, like a person caught in the middle.
夾 is traditionally explained as a person (大) flanked by two smaller people (人) on each side, representing being squeezed or inserted between others.
Picture a large person (大) with two smaller people (人) pressing in from both sides, like a sandwich filling: 夾 means being inserted between.
For キョウ, imagine a person wedged between two others in a narrow alley, shouting 'KYO!' (like 'kyo' in 'kyoto') because they're stuck: KYO -> キョウ.