*As a note there are spoilers all over my examples. So if you haven't read the books or seen the movies and are planning to, you may want to skip all the examples in the middle. I will mark the section with a spoiler warning since I know some people only watch the movies (for shame!) and I will be spoiling the end of the seventh one.*
One thing I learned was the idea of self-reliance, knowing that at some point you're going to have to do something on your own, despite the encouragement and support of friends and family. There's going to come a time when only you can do what needs to be done. It's not going to be easy, it's not going to be fun, but you're going to have to do it.
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This is evident for Harry in pretty much every book. In the Sorcerer's Stone, Ron and Hermione are with him through the trapdoor and the tasks that follow, but after the bottles on the table, Harry has to go alone on to face Voldemort. Hermione gives him encouragement and both she and Ron help him through the tasks that lay before, but he has to get the Sorcerer's Stone and face down Voldemort alone.
In the Chamber of Secrets, Harry has to face Riddle by himself while Ron stays behind and figures out a way to shift the rock from the minor cave-in. Yes, Ginny's there and Fawkes helps blind the basilisk and heal Harry, but Harry is the one who has to figure out how to get rid of Riddle and save Ginny.
In Prisoner of Azkaban, Harry and Hermione go back in time together and both save Buckbeak. But on the lake, Harry is the one who has to cast the Patronus. Hermione tries to help, but this time she just can't. If Harry wasn't able to do it, they'd all be screwed.
In Goblet of Fire, Harry has to do a lot this alone. People help him prepare for the tasks, but he's the one who has to enter the arena and compete. Hermione helps him practice Summoning and "Moody" gives him the hint about flying, but Harry is the one who has to face down the dragon. Cedric gives Harry the clue about his egg, but Harry himself has to save Ron from the mermaids (we need a stronger word for the fierce Amazonian tribe of beings that confronts Harry when he tries to save all those taken. Mermaid sounds too sweet). And then there's the whole maze and Voldemort in the graveyard.
In Order of the Phoenix, Harry has Dumbledore's Army backing him when they enter the ministry. And when Harry takes off after Bellatrix and Voldemort appears, Dumbledore is there to fight him. But Harry is the one to take the brunt of Voldemort's attack when he possesses him. And...(Okay, cards on the table, it's been a while since I read the fifth book. It was really sad to me and I'm not entirely sure I paid attention to exactly what was happening at the end the first time around since I was broken-hearted about Sirius).
In Half-Blood Prince, Dumbledore teaches Harry so much about Voldemort, information that will be vitally important. And Dumbledore gets them into the cave where the Horcrux lies (or used to). But Harry can't rely on Dumbledore for help when he has to feed his mentor the potion in the basin holding the Horcrux. All Harry has is one simple direction and he has to hope that he's doing the right thing.
And in Deathly Hallows, Harry has the ultimate moment of going it alone. He has to walk out in the middle of the Battle of Hogwarts and die so that Voldemort can be defeated. Part of why the scene in the forest is so absolutely heart-breaking is that even though the ghosts of his parents and their dearest friends are with him, he is still utterly alone. This is something only he can do. It's not easy, and it's the last thing he wants to do, but it's the right thing.
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Time and again throughout the books, you find that while Harry has people who love him and help him, there are some things he has to do alone. Things that only he can do. And so when I read him, I learned that there will come a time that I am going to have to make a decision or complete an action on my own. My parents can give me advice, my friends can help get me to the point when I need to do it alone, but ultimately, I have to be the one making the choice in my life. I'm the one who has to do something if I know I need to, not wait for someone else to pick up the slack.
And these books also taught me that it's okay to ask for help when you need it. You don't have to be completely reliant on yourself all the time. Friends and family are there to give advice and stand with you when they can. Like Hermione says to convince Harry that he should ask for help finding the Ravenclaw Horcrux, "You don’t have to do everything alone, Harry."
There are times in our lives when we're going to need to stand on our own two feet. Times when only we can make the decision, take the chance, change our lives. But there will also be times when it's okay to ask for help, to rely on those you love and who you know love you back. And this is one of the best lessons Harry Potter has to teach kids and adults alike.