I think he did but Harry didn’t want to pay attention. Contrast how Harry behaves in those lessons and learning from Lupin, when Harry had problems with the Patronum he turned it inward felt he was doing something wrong and Lupin encouraged him, when he had problems with Occlumency he turned it outwards blaming Snape. It’s hard to teach someone who blames you for every misstep.
RE: OCclumency - Harry was also secretly tempted by the ability to take a peek at things he really wasn’t supposed to be watching - almost like battling an addiction.