Harry learns things the hard way. It isn't that he's thick; he's far from it. But he has to see it break in front of him for him to believe it's broken. Perhaps this stems from loving, feeling, and (too often, in Hermione's opinion) acting blindly. Whatever the reason, Harry has always learned things the hard way.
Harry had to learn the hard way that he belonged with Ginny. It took a series of jealous fits after seeing Ginny with other boys for him to learn he cared for her. But even then he didn't learn he loved her. It took him pushing her away once again and her pulling right back for him to learn he loved her. Many years after the fact, she tells him that if he'd just seen it back in his second year at Hogwarts he would have saved everyone a lot of trouble. But he had to learn it the hard way.
Harry had to learn the hard way that life can go on after loss. The death of his parents didn't really count, as he didn't remember life before they were gone. But he had imagined that he would simply collapse were he to lose someone dear to him. Then he lost Sirius. He still didn't believe he could go on – he merely forced himself forward because he had to. It wasn't until after he lost Dumbledore, Remus, and the rest that he learned that was exactly how life went on. Because it had to.
And Harry had to learn the hard way that he was worth the love he was given. Though he always appreciated Mrs. Weasley's mothering when he was young, he never believed himself to be deserving a mother. If he had deserved a mother, why had fate taken his away? And while he constantly thanked his lucky stars that he were to have two friends – two! - who were the best friends anyone could ever ask for, he waited for the day that their seemingly ironclad trio would fall apart. And while he never could get enough of Ginny's kisses, certainly she would someday come to her senses and realize that just because he was famous didn't make him great. But when Mrs. Weasley continued to mother him through his twenties and beyond, he wondered. And when Harry, Ron, and Hermione's children grew up knowing each other as well as brothers and sisters – after all, their parents were best friends – he dared to hope. And when Ginny slapped him for telling her his fears two days before their wedding day, telling him he'd better think better of her than that if he expected her to stick around, he let out a breath he hadn't realized he'd been holding. And finally, his daughter gets married and she kisses his cheek before she says her wedding vows. Tears fill his eyes, and she whispers, "I love you, Daddy." And then he had finally learns.
If one were to ask Harry, he would say learning the hard way makes you appreciate what you learn. Perhaps he would be right.