CUHK doesn't proffer an etymology. I quote Yellowbridge. How are my two guesses?
Was Ancient China so lawless and unruly that you needed to shield yourself, even when just sauntering?
Did Ancient China rain as China does now, so that you always needed a parasol? In Cantonese, 遮 means parasol. As of today, Three Gorges Dam purportedly is overflowing.