Harry has been lonely since he was a child. He has never felt the love from his family, and he has never experienced the fullness and warmth that fills his heart.
Coming to the wizarding world, to Dumbledore, to the Weasley family, all made him feel new and moved, but he was still lonely, because there was no one among them who was most closely related to his parents. For a boy, especially a father.
And at this time, the big black dog appeared. Even though he was scared, he was still attracted to it. I jumped for joy when Harry learned that Sirius wasn't a villain, but his godfather! After all these years, Harry finally has a real family member, and of course he wants to be with him, forever!
In my heart, the time with Sirius should be the warmest time in Harry's life.
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