"No Exit's" central themes of freedom and responsibility come from Sartre's doctrine that existence precedes essence. Sartre believed that a being-for-itself differed from inanimate objects, or a being-in-itself, since humans have the ability to choose and define their individual characteristics. But with this freedom of choice comes the absolute responsibility for one's action. The fear and anxiety of this responsibility leads many people to ignore both their freedom and their responsibility by letting other people make their choices for them, resulting in bad faith.
This bad faith is what causes Garcin to be unable to leave the room when the door opens. He can't handle the responsibility of confronting his decision to flee his country, and thus leaves it up to Inez to judge him and define his essence. Similarly, Estelle does not think that she exists unless she looks in a mirror, seeing herself as others do. When Inez pretends to be her mirror and says Estelle has a pimple on her face, Estelle's bad faith causes her to accept someone else literally creating her essence.
Both Estelle and Garcin are not only condemned to be free, but are willing to condemn themselves in order to avoid being free.
This emphasis on bad faith establishes Sartre's underlying argument of the play: "Hell is other people." Using only three people and an empty room, Sartre evokes scenes of utter torture and despair. Garcin and Estelle refuse to let go of their pasts, each looking at their friends and loved ones back on earth. They attempt to justify their existence by only thinking about their past experiences: as Garcin explains, his fate is the evaluation of his past actions by other people. Inez however, sees her past as meaningless and inaccessible, choosing to exist in the present instead. Inez...