How does J.B Priestley show, in presentation of Mrs Birling, that she often pretends to be something she is not?

Birling and his wife are indeed middle-class, Priestley tells us in one of his stage directions (though it is never explicitly referred to in the play itself) that Sybil is “a rather cold woman and her husband’s social superior.” Birling is throughout the play ticked down by his wife: early in this act, for instance, for complimenting the servants on the meal in front of a guest. Sybil, presumably from a better social background than Birling, seems to be, in an imperious, passive way, the one in control of the marriage—and of her husband.

In Act II, the Inspector continues to interrogate Mrs. Birling. She, he says, is a prominent member of the Brumley Women’s Charity Organization, to which, it seems, Eva Smith turned for help only two weeks ago. The girl assumed the name “Mrs. Birling” at the meeting, to which Sybil Birling took immediate offense. The girl, who (the Inspector reveals) was pregnant, was desperate and asking the charity for help. Mrs. Birling used her influence over the committee, however, to have her appeal denied. “She came to you for help,” the Inspector continues, “at a time when no woman could have needed it more ... alone, friendless, almost penniless, desperate. She needed not only money, but advice, sympathy, friendliness ... And you slammed the door in her face.”

Mrs. Birling remains imperiously unmoved by the Inspector. “I’ll tell you what I told her,” she says. “Go and look for the father of the child. It’s his responsibility.” Tension builds as the Inspector continues to press, with increasing sternness, for information, and Mrs. Birling tries her best not to give it. Eva did not want to take more money from the father of her child, Mrs. Birling reveals, since Eva thought the money was stolen. Mrs. Birling then firmly restates that the father of the child must be held responsible for the girl’s death, and she tells the Inspector to do his duty.

“Don’t worry, Mrs. Birling. I shall do my duty,” the Inspector replies, and looks at his watch. It gradually dawns on the family—Sheila, naturally, figures it out before her parents do—that Eric Birling was the father of the child. Mrs. Birling, unwittingly, has just pronounced a harsh sentence against her own son.

Mrs. Birling, as the Inspector points out, even managed to avoid giving help and support to Eva while sitting as the chairperson of a committee expressly designed for that purpose. It is not simply a personal misdemeanor, but a public, professional one: both of them symbolize the usual indifference of social organizations toward people in Eva’s position.