I wrote this to explain FLCL to a friend without showing any "ingenuity at guesswork". Just the plain story, which seems more interesting than the symbols to me. Also, I did not do any research to figure out the nonsensical parts of the story. Hope you like it:

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It's just the story of Naota growing up. He pretends to be an adult at first even though he's a child. He's Mamimi's substitute for his older brother, who Mamimi is in love with. That's why she calls him Takkun instead of Naota. (His brother's name is Tasuku.) He's actually in love with Mamimi too, but he does not express it in his attempt to act like a grown-up.

But at the end of Episode 2, TV-kun suddenly joins with him and saves Mamimi from that mecha villain. After saving Mamimi, he accepts that he loves Mamimi and they stare at each other.

All this was symbolized by the boner coming from his head. It's the beginning of adolescence, and all the new sexual feelings that come with it.

The third episode is about his classmate Ninamori. In the beginning, she too pretends that she's an adult. Even though her parents are getting divorced, she pretends she doesn't care about it. She hangs out with the woman her dad is having an affair with.

But the truth is, both Naota and Nanamori want to love and wants to be loved. This is why Naota grows cat ears at the beginning of the episode, signaling the desire to be "petted". (Naturally, he hides it due to his pretense of adulthood.) When Naota reveals in front of the whole class that Nanamori cheated so that she could play heroine with Naota in the school play, Naota's cat ears are transferred to Nanamori. Now everyone knows she wants to be loved. And whenever an FLCL character faces a psychologically stressful situation, they go berserk. (Or the creatures that come out of their head do.)

Thankfully, by the end of the third episode, we can see Nanamori wearing the glasses she never wore (out of fear that people would call her a nerd). She has stopped pretending.

In the fourth episode, for the first time, Naota faces feelings of jealousy. He realizes he's in love with Haruko (the mad Vespa woman). This happens when he sees Haruko seducing his dad for her own gains.

Haruko wants to get the power of the Pirate King Atomsk, but Medical Mechanica has captured him. This is where the show gets murky: Naota has the power to release Atomsk from his head. That is the only reason Haruko is hanging out with him.

But Haruko wanted to see if his dad had the same power. That's why she was seducing him. But it turns out his dad doesn't have that power. So Haruko comes back to Naota and teaches him to use his power (for her own gain). Naota is happy since he's getting Haruko's attention. Cat ears.

Our lovely Mamimi reenters the story in episode 5. Naota is having a chill fight with his father over who gets to have Haruko. Mamimi sees all that and how he's having fun as Haruko teases him. Mamimi is visibly upset.

She tells him how he's become distant from her now. Now he hangs out with Haruko and he controls Atomsk to save the city. Naota enjoys the fact that a woman is jealous over him for the first time. He tries to take her on a date, but she refuses.

The reason becomes clear soon. Mamimi isn't really in love with Naota. He's just a substitute for his brother Tasuku. That's why she refuses to go on a serious date with him.

Seeing this, Naota is pissed off. Our classic gigantic FLCL dick monster shoots out of Naota's head. (Do we need any more clarification that sexual feelings are overflowing in these scenes?) Mamimi starts calling Tasuku's name for help. This pisses Naota off even further. All this time, he has been following his brother to cater to everyone. He's pissed off that no one likes his own identity. He screams, "I will save you, not Tasuku. Never call me Takkun again!" And he uses Atomsk's power to save her. The end.

Oh wait, Atomsk was completely released from Naota's head. Haruko fled with Atomsk and never came back...

Naota is upset that Haruko left her for Atomsk. He also stopped talking with Mamimi since she treats him as a substitute. It's a lonely time. He wears big manly eyebrows to act like an adult and give up on Haruko.

But Haruko comes back. Atomsk disappeared. She needs Naota's help again. Naota is pissed since she left him like that. "You're still a kid," Haruko says, for the first time in a calm way. Naota's rage goes away. He accepts his cat ears and cries. He wants to be loved by Haruko.

Haruko gives him what he wants. Unfortunately, Haruko is doing this solely for her own gain. A new monster created by Medical Mechanica appears. To call back Atomsk, Haruko (for some reason) has to help that monster destroy Earth. He manipulates Naota into doing it.

But Naota summons Atomsk and actually takes complete control of the power. He destroys the monster, but Haruko gets enraged because she wants the power of Atomsk for herself. They fight and Haruko loses. When Naota is supposed to deal his final blow, he transforms back to his human form and tells Haruko, "I love you." Naota, like Nanamori, accepts that he's a child who wants to be loved.

But this time, he also grows a little bit by not giving in to what Haruko wants him to do. He releases Atomsk and Atomsk disappears again. Haruko asks Naota to go with him, but he refuses. Finally, without rushing or pretending, Naota becomes a bit of an adult.

In the last scene, we see him drinking sweet drinks instead of bitter colas. He's also in a uniform unlike before. And the last words Mamimi says before leaving the town is "Goodbye, Naota-kun."