Chief Klough: Those Krauts sure know how to build a boat.
Lieutenant Andrew Tyler: What the hell are you doing, huh? This is not a God damn democracy.
Lt. Commander Mike Dahlgren: Relax gentlemen. She's old... but she'll hold.
Lieutenant Andrew Tyler: His body is gonna to save our lives.
Eddie: It's the first time you ever seen a black man ain't it... get used to it.
Chief Klough: You're the skipper now. And the skipper always knows what to do whether he does or not.
Answer: Technically he's not getting fired, but Dahlgren did not recommend Tyler for his own command, and he won't get a promotion without Dahlgren's recommendation. Therefore, Tyler's only choices are to keep being an executive officer (which is possible but not what he wants, not to mention Tyler feels betrayed by Dahlgren and isn't sure he wants to continue working with him), or leave the navy entirely.
Aerinah