Insights about the ending

An officer is a military leader. Drill Instructor Foley's job is to weed out those who can't hack it as an officer. It's an important job because people's lives in combat are dependent on the quality of the leaders and Foley takes his job seriously.

Foley rightly pegs Mayo as a lowlife loner from the outset -- a wannabe officer -- and therefore puts on the pressure. This is especially so on the one weekend where he has Mayo to himself. Foley does everything he can to make Mayo break AND quit, but Mayo doesn't. He breaks, indeed, but he refuses to quit on the grounds that he has no where to go. At the end of this scene you can see that Foley develops respect for Mayo (which you get a glimpse of earlier when Mayo does extremely well on the obstacle course).

Later, Mayo disregards breaking the record on the obstacle course (which he was definitely able to do) in order to encourage Seegar (the female recruit) to finally makes it over the wall. Foley sees that Mayo's no longer the aloof and selfish loner he was when he rode in on his motorcycle. He's matured; he's developed character. It was already there, of course, but the boot camp training has brought it to the fore, and Foley sees it.

After Worley's tragic death, Mayo confronts Foley while he's drilling the platoon. Foley informs Mayo that they all know what happened and even tells him they're sorry about Worley. He didn't have to do this and it shows that Foley isn't just an honorable man, but also that he cared about Worley. After all, Worley was only one week away from graduating! In a sense, he was one of Foley's kids. In other words, Foley and the platoon were grieving too. But Mayo was closest to Worley and he's crazy with shock & grief at this point. He insists that he's going to quit, to which Foley tells him to meet him for a fight. Sure, there's some testosterone in his words, but he actually does this out of respect for Mayo as a last ditch effort to keep him from dropping out.

And Foley doesn't "kick his axx", as some claim. It was essentially an even match and Foley barely walks off the mat, which is the only reason he technically wins. But that's inconsequential. The purpose of the fight was to run Mayo's steam out so he didn't make a rash decision in an obvious moment of grief & anger. Foley accomplished his purpose. Once Mayo was no longer blinded by rage he makes the right choice and graduates.

This is why he thanks Foley at the end.