Carol Grant’s review published on Letterboxd :
The visual equivalent of punk rock. A rebellious "fuck you" to classical and modern convention, FLCL demolishes the laws of narrative and logic to create an anti-coming of age story, meant to fully encapsulate the fears and existentialism of youth, as well as the stupidity of growing up. All of the adults are more incompetent than the children, large phallic robots literally grow out of a young boy's psyche, bass guitars are weapons of mass destruction, and the shooting stars we optimistically stare at in the sky may actually be plummeting to mark certain doom for our planet. Thinking about the future is destructive, indeed.
It's almost unfair to call it avant-garde because FLCL laughs at the notion of being categorized. Just when we may have a grasp on a character's purpose in the narrative, that character will literally say, "Oh me? I may just be a physical manifestation of your growing sexual urges, as I push you towards adulthood" before laughing off her own purpose and flying back off into space. This kind of self-awareness can come dangerously close to smug self-satisfaction in the hands of lesser directors, but it is instead used here to create a world that exists outside of every known boundary imaginable.
This is a world perceived as "ordinary" by its characters, but is far from it. Only the children and the audience have the gumption to question how this world operates, and for both parties, those questions are all for naught. The world is a random, nonsensical, unfair place, and the only way to survive is to flow with the insanity, lest it (literally) swallow you whole.
Everything is stupid. That doesn't mean we all have to be too.