In the case our Lord the King should go to war again, He learned the arts of riding, fencing, gunnery, And how to scale a fortress—or a nunnery (1.38)
Don Juan's mother wants him to know all the stuff that a man is supposed to know. But little does she realizes that in teaching him this stuff, she's also teaching him to be a womanizer. That's what Byron means when he says that Don Juan will learn how to climb the wall of a nunnery.
His classic studies made a little puzzle, Because of the filthy loves of gods and goddesses, Who in the earlier days raised a bustle, But never put on pantaloons or bodices (1.41)
Donna Inez never educates her son in the classics because she thinks they're too full of sex and violence. But this decision will come back to bite her because Don Juan will go off and learn this stuff by himself anyway.
I never married—but, I think, I know That sons should not be educated so (1.53)
Byron admits that he's never been married, but he's certain that it's better to send young boys to boarding school than teach them at home. In his mind, there's too much risk of parents spoiling their children and failing to discipline them properly.
So first there was a generous emulation, And then there was a general competition, To undertake the orphan's education (12.30)
When Don Juan first shows up in England with a young girl he adopted, everyone tries to win Don Juan over by offering to tutor his little friend. This is just one of the many crafty ways that women try to seduce him. Luckily he's educated enough in the world's ways to see through them.
For a young gentleman's fit education, Though she was far from that leap year, whose leap, In female dates, strikes Time all of a heap (14.52)
Lady Adeline knows that young Don Juan is uneducated in the ways of the world, so she decides she's going to take him under her wing to protect him from aggressive women. We're pretty sure Don Juan knows how to look out for himself by this point.
The Lady Adeline resolved to take Such measures as she thought might best impede The farther progress of this sad mistake. (14.61)
Lady Adeline is pretty aggressive about steering Don Juan's life in the right direction. She even tries to control which women he talks to so she can push him toward the ones she approves of.