Are real leaders made or develop in the classroom or in the field?

Both! The best leaders are constantly learning in the classroom (can be just reading books, doesn't have to be necessarily in that environment) and they apply it to the real world. Information becomes knowledge when you learn it, and becomes wisdom when you apply it.

Take the case of the best martial artists. You can learn the moves, forms, and combinations. But if your intent is to be the next MMA champion, you can only know how good you are when you have to apply it.

I believe leadership is something that is in each of us to some degree but how well that matures or manifests itself is largely a matter of experience, understanding and desire. Leadership techniques can certainly be taught, but true leadership comes from the experience in how those techniques are applied and the willingness to do it.

NEITHER.
Real leaders are made as they learn from daily interactions with the Soldiers around them.
How to build a team.
How to gain unity of effort.
How to address disagreement.
How to remedy a mistake.
How to use diplomacy to gain allies.
How to make a point respectfully, but assertively.
Who to emulate; who not to.

Classrooms can teach the technical aspects. Field work can teach practical application of classroom-learned skills. But leaders can't lead if they don't know how to handle people.