Anime is generally dismissed by mainstream Western society. Common attitudes range from “anime is for children” to “all anime is about women with big tits in giant robots” to “anime is cartoon porn”. How do such contradictory impressions as “porn” and “for children” get applied to the same thing?

Simple: anime is a medium of expression not a genre. It is a vessel and as such contains only what the creators put into it.

It makes no more sense to dismiss the medium of Garden of Words

because it is the medium of Pokemon

than it does to dismiss the medium of Kenneth Branagh’s Hamlet
because it is the medium of a movie based the Thor comic books.

Not that I'm saying Pokemon or Thor are bad; what I'm trying to get across is that not everything in a given medium is for a single audience.

This goes beyond anime movies as well. All of the most moving and thought provoking experiences I’ve had with anime have been those made for television. Here is perhaps the most personal example: Bunny Drop.
Warning, some minor spoilers ahead.

Bunny Drop begins as the story of of Kawachi Daikichi, a 30 year old bachelor salaryman who is attending the funeral of his maternal grandfather. There he sees a mysterious six year old girl, who he learns from his mother is actually his late grandfather’s illegitimate daughter.

This prompts Daikichi to exclaim, “Way to go grandpa!” which earned him a swift scolding from his mother and instantly made him a relatable character. Skipping ahead a bit to the funeral itself, as he’s escorting the girl, Rin, up to the casket to place a white Chrysanthemum on it, she steadfastly refuses and runs into the garden to pick a bunch of Kikyou (bellflowers) to put on the casket instead. The moment makes it crystal clear to Daikichi that Rin is really his grandfather’s daughter, as those Kikyou were his favorite flowers. Later, after the ceremony, when all of his relatives are giving excuses about why they cannot take in Rin, who’s mother has abandoned her, and how they should give her to a government agency, Daikichi puts them all to shame by declaring that he’ll take her in and raise her.

The entire episode is wonderful as it not only gradually builds up Daikichi’s character but also I got to see his feelings towards Rin shift from curiosity to genuine affection and attachment. Add to that how he steps up to do the right thing when no one else will, and in fact his family is actively telling him not to, endeared him to me.

That is not the moment I most want to tell you about though. It is in a later episode, after Rin and Daikichi have been living with each other for a while and they have formed a real relationship, that came my favorite moment. Daikichi has been debating formally adopting Rin and he finally works up to asking her if she would like to become his daughter. Rin… tells him no. You see this look of utter bewilderment on his face and you can see how badly it has hurt him that this girl he loves so deeply doesn’t want him for a father.

He then asks her, “Don’t you think it would be better if you had a father?” Rin tells him that she wants to stay her father’s daughter and that it’s important to keep his surname and that “Daikichi should stay Daikichi.” He’s so deeply moved he actually starts to cry. I don’t know that I’ve ever felt as connected to a character on my television set as I have at that moment.

Experiences like that are what I think people are missing out on.

If I've peaked your interest, you can legally watch Bunny Drop for free online at http://www.crunchyroll.com/usagi-drop