Can someone fully explain Foley's dislike of Mayo?

Ok, there is a bit of a misconception about the training presented in the film. this is not "boot camp," it's Officer Candidate School. There is a big difference, though the ultimate goal is the same, to transform a civilian individual into a professional serviceman. These men and women are being trained to be leaders, not just sailors or soldiers. Candidates undergo a rigorous screening process and must have certain prerequisites, including a college degree, from an accredited school, and possess an minimum GPA. They have to pass a physical and must take an exam and pass with a minumum score. They also have to go through an interview process. Now, at the time of the film, the Navy was undergoing a huge expansion period, so there was a big push to increase numbers. I started the NROTC program just after the movie was released and was part of a big incoming class. It's possible Mayo's background around the Navy would have helped compensate for academic deficiencies, but I suspect he was sharp enough to get decent grades in college, earned or not.

Foley's dislike stems from Mayo's lack of discipline, his lack of leadership, and his unwillingness to become part of a team. He recognized Mayo was only in it for Mayo and would most likely never work well as a team. I think he suspected that Mayo believed he could be off by himself as a pilot, rather than flying with a wingman and as part of a squadron, and that Mayo didn't understand the leadership component of being an officer. Sid had the leadership skills, but not the confidence or the psychological stability to be a pilot. Caruso's character was too afraid of the dangers of flying. Segar wanted to be there more than anyone and wouldn't quit. Foley spots this and pushes her to push herself, or she will never make it. In the dunker scene, he is both complimenting her and telling her that she still has to get past her chief barrier.

Foley's job is to weed out the candidates who don't have the material and push those that do into discovering their talents. With Mayo, he sees the liabilities, not strengths, until he pushes Mayo into admitting why he is really here and getting him to see what the program is really about. After that, Mayo begins to understand that he is part of a team and a family, something he never had. Paula is also teaching him about being part of something other than just himself, as is Sid and Segar.

This film is one of the most accurate depictions of military training you will ever find; in part becasue of the screenwriter's personal experience, and Taylor Hackford's refusal to make changes to meet the Navy's projected image. It's a warts-and-all look, and the miltary isn't fond of showing the underside of itself.

Stuff like Full Metal Jacket notwithstanding, the DIs aren't being sadistic, usually; people's lives depend on their working as a team and carrying out viatl orders with split-second reaction. They have to instill military discipline quickly, and this is a tried and true method. Various DIs will have different styles, but the harsh commands are designed to grab attention and respect immediately. In susbequent years, the regulations governing the conduct of DIs has gotten much more stringent and someone like R Lee Ermy in FMJ would likely find himself brought up on charges after punching a recruit (unless in self defense). Foley's fight with Mayo would likely bring trouble, though I suspect any investigation would be met with silence from everyone. Even with tighter regulations, a determined DI can find a way to instill "discipline" in private heck, I know of one ship's captain, who during Captain's Mast (non-judicial punishment), was sick and tired of a sailors beligerent and disrespectufl attitude that he had everyone clear his stateroom, except the offender. All that was heard from outside was a loud smack and an equally loud thump. Everyone was called back in and the Master at Arms (navy cop) was directed to "Remove this POS from my stateroom." It didn't take much of an imagination to determine what happened, but there was no evidence for an investigation, nor was anyone likely to testify against the skipper. Most probably applauded what he did.

"Fortunately, Ah keep mah feathers numbered for just such an emergency!"

As Foley said to the candidates on the first day of OTS, "I will use every means fair and unfair to trip you up and expose your weaknesses."