STINGER: Your family name ain't the best in the Navy.
Maverick has no family, only a family name that "ain't the best." We learn more as the film goes on, but it's clear early on that somebody in Maverick's family has tarnished the Mitchell name, and made things hard for Maverick.
ICEMAN: Sorry to hear about Cougar. He and I were like brothers in flight school.
Iceman's relationship with Cougar defines the familiar nature of the Navy pilots. They're a team, a group of brothers, a family. Maverick and Iceman, however, don't accept the fact that they're "related" until the end of the film.
GOOSE: Look, man, I know it's gotta be tough for you. They wouldn't let you in the academy because you're Duke Mitchell's kid and you have to live with that reputation.
Family can be a huge burden. Family can even affect your life even when, in reality, you're not at all responsible. Maverick isn't admitted to the Naval academy because of his father. Hey, that's not Maverick's fault.
MAVERICK: You're the only family I've got.
While Maverick takes the Navy-as-family thing seriously (Goose is his family), he's also a loner, a black sheep. The fact that he only considers Goose a family member is part of his problem, and the source of some of his arrogance.
VIPER: You're a lot like he was. Only better, and worse. He was a natural, heroic son of a b****, that one.
Maverick is defined by his father in more ways than one. Not only does his legacy haunt him, he, apparently, acts and flies just like him, even though he died when Maverick was very young.