Open doors: figuratively associated with possibility and opportunity--tied to the future. Literally, they appear welcoming, friendly. Open doors beckon. They imply trust and connectedness.
Closed doors: quite the oposite. Figuratively they represent rejected possibilities, options that have become unavailable--tied to the past. Literally, closed doors can appear aloof and impersonal, possibly even forbidding. They exhude division, reinforcing distinctions of in vs. out, public vs. private.
Doors do it all. Sometimes open, sometimes closed. Welcoming here, forbidding there. Allowing this but prohibiting that. And always the possibility of change, that a closed door will one day open or an open door swing difinitively shut.
Interesting, that doors can do so very much.