Strongly associated with the Han-dynasty policy 罢黜百家,独尊儒术 — 'dismiss the hundred schools, revere only Confucianism.' The word still carries that flavor of officially stripping someone of rank or status.
The black radical on the left. It carries the idea of being blackened or blotted out — to be dismissed is to have one's name struck off in disgrace, a fitting semantic match.
Gives the sound (chū close to chù) and reinforces the meaning: to be dismissed is to be put out of office. A rare case where the phonetic also nudges the sense.