Besides 'facile' and 'facility', there are a few other words from the same root: 'faculty', 'facultative', 'facilitate'.
It is pretty common for words to diverge in meaning and drop old connotations as they find distinct niches.
It is pretty common for words to diverge in meaning and drop old connotations as they find distinct niches.
In Latin (and thence English) facultas meant ability, while facilitas meant easiness.
The adjective facilis comes from the verb facio (to make or do; from the same PIE root as the English verb 'do'), and meant something that can be done/made; something easy, ready, or quick; or someone friendly, courteous, or compliant.