the problem with gender roles
Gender roles, despite existing wherever humans live together, can be oppressive and even harmful. A man can have a gentle and motherly character and be unable to express it because it is too "feminine." A woman can be athletic and stoic and people will call her a "tomboy." Women who dress in a masculine way are often thrown out of women's bathrooms. Men who dress in feminine ways are laughed at, bullied, or worse.
When taken to an extreme, upholding gender conformity can cause violence and death. Trans women are assaulted and killed for simply being trans. Gay men and lesbians are also victims of violence because they are not attracted to the gender they are "supposed" to be attracted to. There are many structures, institutions, and beliefs that try to keep men and women in neat, separate boxes.
When someone breaks out of the box, they are met with ridicule, disdain, and violence, with the ultimate goal of forcing them to conform. Gender roles limit what any person can do, and reduce a person's life to what he/she "should" do. It forces people to perform what is expected of them, rather than live authentically as who they feel they are.
Gender nonconformity is simply not conforming to gender roles. In practice, it can mean things as simple as a woman wearing a tie, or something as complex and life-changing as transitioning from one gender to another. There are obvious problems with using "nonconformity" as a way to describe people who don't follow gender norms. It implies that conformity is a good and desirable thing, rather than something that harms everyone.
Most of us have something nonconforming about the way we live and express our gender. Some women don't wear makeup but otherwise dress feminine. Some men prefer to be stay-at-home dads.
Living out every gender norm in our culture is an impossible task. However, researchers of gender and gender norms have known for a long time that seeing transgression of gender norms makes people uncomfortable. People who transgress gender norms are also seen as being lower in social status, not being straight, and having values that are radically different from our own.
This discomfort comes from an ingrained human need to categorize people. And the most essential category we have for classifying humans is gender: is this person a man or a woman? This categorization allows a lot of other judgments to be made: if this person is dangerous, if this person is a potential mate, what this person possibly does for a living, and more. When we meet someone we can't categorize easily, we generally react with discomfort and confusion.