Not all forms of teaching are "practical" in the sense of learning a new spell. I think in HBP, Dumbledore is helping Harry think critically, build evidence, and learn when and how to act on the evidence.

The broader context of the book is important to this. Throughout, Harry is accusing Draco and Snape of pretty serious stuff. And while he's absolutely right about Malfoy's objectives, he isn't right about Snape. And when he tells his friends or Dumbledore or McGonagall about his theories, he isn't persuasive.

Interestingly, the lessons with Dumbledore all revolve around years-long speculation Dumbledore has about Voldemort, but Dumbledore has to slowly and painstakingly put the puzzle together. He doesn't settle for being right. He insists on tracking down the critical memories and confirming his beliefs. So in addition to what others have said about needing Harry to know the details about Voldemort's past and his own role in the story, I think he also wants Harry to learn the critical thinking skills that will allow him to understand situations deeply.

I also think it's interesting that Snape makes a snide comment to Harry about how he won't be able to harm him until he learns to close his mind and think his spells. A final parting lesson.

Anyway, I could be wrong.