Daijo-bu?!

F
LCL plot wise can't really be explained thoroughly like the majority of animes like this one. The series leads from one thing
to another, and senseless things pop up to probably take up the time needed for one episode (which is about 20 to 24 minutes). If the show didn't have that, then it would probably be a five minute special!

So, what I've done is, watched the series over and over again 
(well, probably three times) to jot down key elements to explain " what the hell FLCL is about ", and to also explain some " weird " things.

Warnings: SPOILERS

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  The " True " Plot

  
FLCL is about, basically, about kids coming into 
adolescences. This can be proven in the last scene of the last episode. Naota (or Taro, Ta), is coming into a point in his life where he is not going to be a kid anymore, and dealing with the fact that one day he will have to grow up into an adult. This realization is thrown in his face many times through out the 
series, such examples are in episodes four, five, and six. The characters influence this onto Naota, and while he deals with 
that fact, himself dose, mentally, change into a teenager as the antics of his father and Naota throughout the household make 
him release to become something better than his childish father. The series also shows how other people, though probably not going through the same thing as Naota, try to escape the pain 
of their own families. All of them feel as if they are locked and trapped in the city with the factory ontop of the hill that blows 
out smoke at a certain time of the day. Naota, even though he hates his brother for what he done, still envies him for being able to finally leave the city that he feels trapped in. His insecurities 
about life in general take the best of him, and I feel that's 
one of the things that make FLCL what it is, forgetting all 
of the insanity.

   The Nazi Father (not literally)

  
In episode five, Naota's father is wearing a Nazi uniform during the duel. Which, really, shocked me. But then I began to realize that Japan was apart of the Axis powers (German, Japan, Italy) during WWII, and the way that his father personality is like, it would be obvious that he would do something as crazy as that. I also began to think that it would have something to do with the gun that he was using during that duel against Naota over Haruko's " love ". Now, from watching the fansub, there was 
some Kanji on the bottom when his father began to run with 
those two guns, so I don't know if it was the name of his attack (such examples: Ronin Warriors, Yu Yu Hakusho) or just some explanation towards this.

    The Attack of the Pigeons!

   In episode five (i guess you can see that this is my favorite episode) the duel is interrupted by Naota and his Grandfather, back to the house, when they are watching TV. This scene leads up to why Naota and his father are fighting each other. But anyway, while watching TV, there is a guy talking about something serious, then all of a sudden the guy then talks about killer pigeons, this obviously is taking this from Alfred Hitchcock's The Birds, especially when the TV explodes and pigeons fly out
of the television.

   South Park - FLCL Style

  
This is pretty much self explanitory, but I'll add it in here for 
the hell of it. In episode 5, again, Kitsurubami is talking to 
Amarao while looking for the target to " snipe ". Amarao is supposedly at a hair salon, and is getting his eyebrows done. Now, the scenes switch back and forth, so there isn't much use for the plot. But, if you can really listen, you can here how the seiyuu rises his voice a bit higher and talks a lot faster to imitate the South Park cast (which is like, five people since Matt Stone and Trey Parker do the majority of the voices), and the style. 
This probably must explain that South Park is probably popular
in Japan too.

    The Music and the Relation to the " True " plot

   
The music, or the songs by The Pillows, have strong lyrics
that relate to the series, especially the song " Little Busters " (played at the last episode for the last scene).

    We're the kids think of the future
    Maybe kids don't need their masters

     Those lyrics maybe wrong, but I can't understand engrish 
that well. Sorry, The Pillows, you sing in english good... its just this song! Many other songs, such as Subhuman and Advice 
bring out the emotions that Naota feels.

     I want to see you again someday... ooohh ohhh
    So leave me alone away with you! Ooooh.... ooohh!
    Yeah! Yeah! Yeah!

     That was from " Advice " and probably explains what Naota thinks of Haruko. But not all the songs surround Naota, some circle Haruko and other characters, like Hybrid Rainbows and I Think I Can.

     Mister Monkey!

    
Naota's father makes a reference to Lupin by the way he is dressed. He asks his father on which version is better, the blue jacket version from the first season or the red jacket from the Castle of Cagliostro. They also make a reference to a person named " Mr. Monkey ", now from what I know, Mister Monkey
is a North American cosplayer that looks EXACTLY like Lupin,
so a lot of cosplayers who cosplay as Lupin look up to this guy.

    Naota: Why are you dressed up like that for?
    Father: Oh, you mean, ala second tv series? Heh, do you prefer the blue jacket from the first series, or Castle of Caglistro.
    Grandfather: You've got taste, I must confess.
    Father: But, Mr. Monkey says himself, that the red jacket is the correct one. So this is how it has to be, whether " He " likes it  or not. Hey, Naota-kun, where are you goin? Naota-kun
!