陈腐 attacks ideas, language, customs, or institutions as both old AND no longer worthwhile — "stale and rotten." Compare 陈旧 (chénjiù, old / outdated, neutral-to-negative) and 老套 (lǎotào, clichéd, more conversational).
memory
陈 = aged / stale (as in 陈酒 aged wine, but here negatively); 腐 = rotten / decayed. Aged + rotten = something that has sat too long and gone bad — perfect for stale ideas.