Some anime are just absolutely bewildering. Whether it's an abstract anime that's rife with symbolism, like Mawaru-Penguindrum, or an incessantly violent program with a convoluted plot, like Dead Leaves, these confusing anime are likely to leave you scratching your head.
Note that confusing doesn't automatically imply a lower degree of quality. In fact, some of the best anime ever made, like Neon Genesis Evangelion and FLCL, are difficult to understand without background knowledge and careful thought. These series are still worth watching, but it's best to do so with the understanding that they might not make sense on the first viewing, if at all.
These series are not just simple anime to relax with and have on in the background. These are challenging and complex programs that demand total attention and commitment.
FLCL is one of the trippiest anime ever made, so while it's enjoyable whether you understand it or not, it not an easy watch. On a thematic level, it's a coming-of-age story, but on a literal level, it's about a pink-haired alien who opens up a portal in a 12-year-old's forehead and pulls robots out of it. Teasing out the actual meaning of this utterly insane anime is easier said than done.
Pop Team Epic
Pop Team Epic is for viewers who are unaffected by the lack of a plot. This ridiculous anime features two main characters, Pipimi and Popuko, who have few distinct attributes aside from Popuko being slightly more aggressive than Pipimi. Instead of telling a story, the anime flits between increasingly bizarre sketches involving the two.
In one sketch, they might be mob bosses; in another, they're Pokémon. Because most of the jokes are references to aspects of Japanese pop culture that are a lot more obscure than Pokémon, the specifics can often elude Western viewers.
Though Steins;Gate does eventually start to make sense, the beginning utterly baffles a huge portion of its audience. The first episode is a whirlwind of unanswered questions. Depending on what kind of viewer you are, that might leave you hungering to get those questions answered, but it also might make you too confused to want to continue. Beyond episode 1, it can be difficult to keep track of what happens during which timeline, given the show's heavy reliance on time travel.
While Higurashi: When They Cry certainly makes an impression with its gory torture scenes, the reasons behind them aren't always clear. Some characters are brutalizing others because of child abuse, some are forced to participate in strange religious rituals, and some suffer from Hinamizawa syndrome, a fictional psychiatric condition that causes murderous urges.
It's hard to keep track of who is attacking who for what reason, both because of the actual complexity and because after a while, your brain might go numb from all the bloody scenes.