The traditional 門 is unmistakably two saloon-style door leaves; the simplified 门 keeps the frame in three strokes. It's one of the most productive radicals: whatever happens, happens at the gate — 问 (ask: a mouth at the door), 间 (between: sun through the gap), 闻 (hear: an ear at the door).
门 organizes Chinese space and society: 开门 (open the door — also 'we're open!'), 出门 (head out), 门口 (doorway). Tiananmen (天安门) is the 'Gate of Heavenly Peace'. Socially, 没门儿! ('no door!') means 'no way!', and a respected school of thought is a 门派. Feng shui obsesses over doors — where fortune enters. Three strokes, and half of Chinese life passes through them.
Two door leaves on a frame — the DOOR.
没门儿! 'there's no door!' = 'absolutely no way!' — refusal, architecturally speaking.