Introduction: It's not just you
You may have children who love anime, Japanese animated cartoons. You may even have started watching them for your own amusement. There are many paths to wisdom. If you have watched anime, you may have found them to be incomprehensible; if so, you are missing the point.
Anime isn't supposed to be comprehensible: it's existential! It's Camus for kiddies, Sartre for tweens! Zen for those under 10! Don't believe me? Consider:
The plots make no sense.
Watch from the beginning. Take notes. It doesn't matter. By the second episode, it will be impossible for you to say with any certainty who the characters are, what their motivation is or how their actions have any meaning within the context of their stories.
And, just when you think you have been able to make some sense out of bits and pieces of the story, an arbitrary plot twist will come along to make nonsense of everything that had gone before it; everything you thought you understood will turn out to be something completely different. Just like life.
Audiences steeped in Aristotelian verities about narrative structure will be sorely disappointed. However, audiences who understand life as a series of random events without structure or purpose will feel right at home watching anime.
The characters' eyes are unnaturally big.
You may have thought that this was just a stylistic affectation. Well, that may be, but it's a stylistic affectation with a deeper purpose: to undermine our ideas of seeing as believing, our faith in the power of human visual perception. It doesn't matter how big our eyes are - they could dominate our faces - hell, they could be our faces - and we would still not be able to clearly see what was in front of them.
The characters' hair is unusually spiky.
It gets so ridiculous that you can be forgiven for thinking that as much as half of each show's budget is spent on hair gel. Still, if you approach anime with an awareness of its true existential nature, you can appreciate each character's hair in a whole new way: as metaphor. To wit:
Spiky hair = spiky personality
The hair of characters is a representation of the turmoil that roils within each of them, and a reminder that no matter how close we get to other people, they can always surprise us with sharp, nasty hidden depths.
Characters' lips don't synch up with their voices.
This is often attributed to poor dubbing. That may be true in a technical sense, but it doesn't mean that it can't also have existential significance.
It is clear that there is often a disconnect between what people say and the way they behave; this is sometimes referred to as "cognitive assholnance." The fact that the lips of characters in anime do not synch up with their voices visually foregrounds what is usually an internal process.
It can also be creepy as hell. Just like life.
The plots really make no sense. None at all. Really. Are you still trying to find some sense in the narrative? Forget about it. You won't.
Human beings are story seeking machines: we do our best to find meaning in even the most disparate events. However, as somebody who may have been Winston Churchill once said: "If a man is not trying to find the plot of an anime series by the time it has aired its second episode, he has no heart. If he is still trying to find the plot of an anime series by the time it has aired its fourth, he has no brain."
Anime is really for young people on drugs.
You had Fritz the Cat, your kids have Dragonball Z. Fair is fair.
Conclusion: Best just to go with it.
The best way to watch anime is to treat it like walking into a sauna: just let the warmth of its hallucinatory imagery carry you away. Don't worry if your skin gets flushed; it's all part of the process. And, if worse comes to worst, always be prepared to run outside and roll around naked in the snow.
You may object that children raised on anime will become a generation of nihilists. The only response to this is: have you seen the shape of the world lately?