STINGER: Let's not bulls*** Maverick, your family name ain't the best in the Navy. You need to be doing it better and cleaner than the other guy.
Can we blame Maverick for being obsessed with his family name? Stinger is probably the billionth person to remind Maverick of the Mitchell family history, and to call him out for not redeeming that past by flying better.
GOOSE: But it's like every time we go up there, it's like you're flying against a ghost. It makes me nervous.
The "ghost" Maverick flies against is his father, and his father's reputation. That family past is a huge burden for Maverick, and it makes him one dangerous pilot. It also affects his teammates. He needs to move beyond that past.
MAVERICK: The stink of it was, he screwed up. No way. My old man was a great fighter pilot. But who the hell knows it's classified? It's all classified.
Maverick is really irritated when he tells Charlie this story, and that's because, as we've already figured out, he's hug up on the past. Every time he thinks about it, he gets worked up ("But who the hell knows"), partly because he doesn't know the truth.
VIPER: You gotta let him go.
Viper is worried that Goose's memory will become a huge burden for Maverick, and this is why he tells him that he has to let Goose go. The problem is, he tells Maverick to do this about ten minutes after Goose's death. That's a little unreasonable