Give that guy some points for vocabulary! He could have said you were putting on a front by faking modesty, which would be one way to describe demure behavior. You also could be considered demure if you're modest or bashful and not pretending.
Some guy I don't like told his friend I was acting all demure. What does that mean?
Demure often appears in works of literature — both classic and modern.
In Vanity Fair, William Makepeace Thackeray writes,
She cast down her eyes demurely and smiled as they started away from her; Emmy scurrying off on the arm of George (now grown a dashing young gentleman) . . .
In another chapter, he writes,
Both of them were rather agitated, and thinking of old times. He about Eton, and his mother, whom he remembered, a frigid demure woman . . .
From Sinclair Lewis's Babbit:
. . . Babbitt sat creakily back in his revolving desk-chair and beamed on Miss McGoun. He was conscious of her as a girl, of black bobbed hair against demure cheeks.
The same author also wrote, in his novel Main Street,
. . . at two minutes to five a town of demure courtyards and welcoming dormer windows had been erected, and at two minutes past five the entire town was as flat as Babylon.