What does Anna Quindlen mean when she writes about "Our Peculiar Standards of Masculinity"?
I assume that you are asking about Quindlen's line in her essay about school shootings that is in the link below. If so, what Quindlen means by this is that we here in America have strange ideas ("peculiar standards") as to what it means to be a man ("masculinity").
Quindlen points out that Kip Kinkel's father did not believe in psychological therapy. Instead, he thought that he could take care of his son's problems by doing things like buying him a gun. Quindlen says that this shows that we have strange ideas about what it means to be a man. We think that men do not go to therapy to have their feelings examined. Instead, men do aggressive and violent things to prove their masculinity. For this reason, Kinkel's father thought that a gun would do his son more good than therapy would.
So, Quindlen is using this phrase to say that Americans have (in her opinion) strange and counterproductive visions of what men should be.