Present participle of egress; the act of moving out of or exiting a location.
From egress (verb) plus the present participle suffix -ing, which comes from Old English and marks ongoing action.
Technical and formal—you won't hear 'egressing' in casual speech, but emergency procedure manuals love it because it sounds precise and official, which is exactly what safety communication needs.
Complete word intelligence in one call. Free tier — 50 lookups/day.