Pushiness is a quality of being impudent, rude, or offensively blunt. Your cousin's pushiness is evident in the way she constantly grabs the remote out of her hand and insists on watching only her favorite shows.
If someone has no qualms about getting what they want, even if that means acting mean or aggressive, they're in touch with their pushiness. When you shop for a new TV, a salesperson's pushiness may make you decide to buy one online instead. And the pushiness of parents who think their kids deserve better grades may cause a teacher to dread parent-teacher conferences. This noun comes from pushy, a 19th-century adjective meaning "overly aggressive."