I think this is one of the most depressing parts of the anime, especially with Misty. She’s normally a fiery, headstrong, and sweet kind of person but this is one of the only times where you get to see her so vulnerable. If you saw Gotta Catch Ya Later, you can tell Misty didn’t really want to leave while her friends and family still get to travel around to wherever their hearts desire. But not her. No matter how you look at it, it’s a sucky situation.
I think the writers and animators did a great job displaying a different side of Misty in contrast from her usual sweet and tomboyish nature. Adding to the mix people are threatening to take her home away from her and has to prove herself capable of being a gym leader in a very short amount of time. Not to mention, she has to deal with one of her greatest childhood fears. (To clarify, Misty was nearly eaten as a baby by a Gyarados.) Misty is overwhelmed by the amount of responsibility placed on her shoulders. She looks helpless and lost without the presence of her friends. But I think her dream represents her sadness of how much she wished to travel with her friends. She feels more confident with Ash and Brock around because they always have a solution to everything. In this scene, she truly does feel alone. I think Gyarados represents responsibility because of the way it wrapped itself around Misty’s leg, reminding Misty she cannot leave whenever she wants to anymore. She feels trapped and feels like she failed to be a decent gym leader.
Even though Misty has constantly proved herself to be capable (Princess Cup, Whirl Cup, Seaking Catching Contest, Tour de Altomare, etc.), she was obviously not ready to be given full responsibility of the Cerulean Gym. I think she knew handling the gym would go to her eventually, but not at such a young age. Her sisters knew she could handle anything and figured Misty running the gym would be no big deal. They were very inconsiderate not to wait for Misty to return before leaving the gym vulnerable, but what else is new with them?
It really makes me wonder how long has Misty spent alone before meeting up with Ash. Judging from her sisters’ reaction in The Waterflowers of Cerulean City, Misty’s departure from the gym prior to meeting Ash was fairly recent. I think the reason why Misty really left was because she barely connected to her sisters. Misty at first describes Cerulean to be an old place no one wants to go to and tries to persuade Ash going to Vermillion was a much better option. It makes me think she was always belittled by her sisters and the way other people saw her (confirmed by Dorian in the episode Just Add Water). Another reason may be because her sisters simply handed out badges whenever they didn’t like battling. I highly doubt Misty approved of their form of battling. So she runs away to try to catch more water pokemon and prove that she’s more than just a “runt”. This may be why Misty is disappointed to find her big catch was a boy and his Pikachu.
… I’m rambling too much now.