Ika Musume is a Puppeteer Parasite.The "squid hat" is the real Ika Musume. When she decided to invade the surface she realized that she would need a body that could function on land, and to that end she attacked some poor, anonymous swimmer and latched onto them headcrab style. This would explain a number of oddities within the series, all of which have been pointed out as unusual by the characters themselves:
Ika Musume is a sea goddess.One of the Japanese myriad Gods (Kami). It's just that she doesn't know she is one. She naturally gathers the attention and affections of those around her (faith), the particular beach she's staying at is clearly a lot safer with her around, and she even seems to bring varying amounts of luck to those around her.
The Data Entity sent Chizuru to observe Ika.
Ika misunderstood the mission for going to the surface in the first place.Ika is the only squid person we see in the show. Who's to say that taking over the world isn't what others instructed her to do? As naive and easily-distracted as she is, she misinterpreted what her original purpose was for going on land. The pollution reason could very well have formed in her head.
Ika is Obfuscating Stupidity without realizing it.Inside Ika is something that really is your standard gigantic, evil, Lovecraftian Eldritch Abomination, and she only needs a stimulus to wake it up so she can realistically take over the world! It will reveal itself in the anime finale.
Ika is the result of a tentacle monster and a school girl... nuff' said
Ika is the daughter of the great Cthulhu
The show is a prequel to Frank Schätzings "The Swarm"Ika Musume is the first attempt of the Yrr to get rid of humanity by sending a genetically engineered organism on shore. It won't work out so well, so they will decide to go for murderous whales and crustances filled with biological weapons instead.
Pre-brainwashed Ika was Yotsuba!Expanding on the hat parasite theory.
The siblings' parents are dead.Chizuru is the apparently the oldest sibling of the three (having evidently graduated from school, probably a ninja school or something like that, that's why she knows all this martial arts stuff), but yet does not look all that much older than middle child Eiko. However, Eiko is the only one of the two who is shown to be going to high school, which is neither compulsory nor free in Japan. The Lemon Beach house, while fairly successful, seems to be their only source of income which means that it would be difficult (maybe disastrous) for both girls to go to school AND run the place long enough to make enough money to go through the month. Takeru is an elementary school kid, so he can't run the place by himself, and no parents around means they can't run it. Since squid die after they mate, Ika Musume has no concept of parents and so doesn't question the fact that they apparently don't have any around. Gorou may not see any reason to question anything since he and Eiko are childhood friends. Sanae is their next-door neighbor and another one of Eiko's friends so she feels no need to question anything either. As for Nagisa, there's no explanation for her not to question their lack of parents other than not doing so out of politeness.
Chizuru from Negima and Chizuru from Ika have common ancestor.Which they are obviously named after. If said ancestor is still alive - she is scariest grandma EVER!
This series takes place in the same universe as TouhouIka is a squid youkai. She even has a hat!
Ika Musume is the daughter of Ikadevil.Fo' shizzle.
Ika Musume was sent to "invade" the surface for her own goodWhatever she really is she's more like a human than a squid, and the others felt she would be happier among humans. They called it an invasion so that it wouldn't seem like they were kicking her out.
Mini-Ika is real.The first time we're introduced to Mini-Ika, it's revealed to be Sanae's Dream. However, in season 2 we're treated to a second adventure of Mini-Ika, seemingly within the same framework of the original dream. Except this time it was Gorou's dream, not Sanae's. Both of them are perceiving a parallel world in which Mini-Ika truly exists.
Kozu Tanake tried to take over the world once.In the episode in which Ika was losing her squid abilities, a myseterious girl comes to her and discusses humanity with her. She then pretty much said that humans weren't that bad. And then she tells her that she wasn't alone. You could get the implication that she also came from the sea and probably viewed humans as Ika did. Like Ika, she tried to take over the surface world as vengeance on humanity for polluting the sea. However, during her life, perhaps she met some humans that weren't as bad as she thought they were and made a Heel-Face Turn. This could explain her comments about humanity and her telling Squid Girl that she wasn't alone.
Ayumi is awkward around normal humans......because she isn't a normal human herself and probably suffered persecution from humans, so she won't be able to act normally around normal people, but Ika Musume (anthropomorphic squid) and Chizuru (superhuman strength, agility, durability and reflexes) and Sanae (alien, see below) are OK. But who is she?!
Sanae is an alienSince even a broken (analogue) clock shows the time right two times a day, Cindy accurately guessed, that Sanae is an alien. Ayumi did sense it too, since she's comfortable around Sanae. Sanae was afraid, that her cover was blown by Cindy and tried to threaten her into silence. She did later manipulate Cindy into forgetting her suspicion. She is probably another Arume scout besides Hagino, who was sent to investigate these strange rumors about Ika Musume, since they couldn't have anyone other then themselves conquer Earth. She investigated the case and found her no threat to the coming Arume invasion. But, as her co-scout, she fell in love with an Earth humanoid, namely with Ika Musume. She gave false reports to her superiors, so she wouldn't on the hand have to assassinate Ika Musume, but also wouldn't have to leave her.
The unknown thing inside the hat, is actually the same unknown thing in Kamijou's right hand.Because why not? It's a mystery anyway.
Ika Musume is the descendant of Uric the Oddball from Harry PotterJust read the article at the HP wikia.
Ika Musume and/or Kozu Tanake is/are related to Davy Jones.They're all humanoids with cephalopod qualities. Ika, Kozu, or both are the descendents of Davy Jones and Calypso. Ika's disdain of humans may stem from the relationship between Davy and Cutler Beckett and the EITC. One of them may become the captain of the Dutchmen after Will Turner.