We've all seen plenty of these kinds of memes like the one above. The protestation against hearing people dismiss anime as being 'just for kids' is a strong one for many anime fans, something that we tend to jump at as a worldwide community.
I totally get it and I've been there myself, defending anime against people who say it's for kids. Generally the people who say that are people who've never watched anime and probably who don't even consider themselves fans of American cartoons either. So you jump to defend the medium, listing whatever examples you choose to show that anime is not for kids. I get it.
Really, though, when you think about it a little harder, take a step back, you have to acknowledge the problem with this argument. It shouldn't be that people lash out against this dismissal. Instead, be rational and calm. The fact is that yeah, some anime IS for kids.
Before anyone wants to jump down my throat about that claim, just consider it. The same way that any artistic medium is broken up into separate and distinct genres, so is anime. People, both fans of anime and not, are quick to consider anime a genre of animation instead of an entirely different animated medium.
There are any number of different kinds of anime, from cutesy Slice of Life stories to hardcore, mature Seinen stories. This means that yes, anime are drawn and conceived with a specific audience in mind just like any other work. Some of the audiences will be kids, or teens (young adults if you want to be vague).
For example, Fairy Tail is 100% a manga/anime for young adults. All shonen anime are, it's a focal point of that genre of anime. It certainly handles some mature issues, but the same way that other shows for young adults do. Young Justice tackled some of the same stuff. Young adults are the MCs in all of these. Naruto, Bleach, Dragon Ball, HxH, One Piece are all shonen anime with an intended audience of young adults.
Of course that isn't to say older folk can't enjoy them too, but that's the target demographic there.
Then you have Seinen stories, like Black Lagoon, Berserk, Tokyo Ghoul, or Mushishi. These are stories with adult characters (or at least late teens, early 20s) dealing with issues with more gravity and handling a more 'mature' perspective. None of the flashiness of typical shonen battle mangas. Tokyo Ghoul straddles the line, but with the significant level of torture and violent death, it is definitively seinen.
It is frustrating to hear people outright dismiss anime as an artistic medium when they reject it as being 'just for kids'. It is diminishing of something that artists work hard at and that fans take very seriously at any age. However, lashing out at that person isn't going to solve anything. Flat out saying anime isn't for kids isn't helping either.
Instead, the next time someone says this, just say "Yeah, some of it is, sure. But not all of it." The same argument can be leveled against American cartoons. Would you say that Archer is a show for kids, just because it's animated? How about South Park? Or Rick and Morty? People who dismiss anime as being for kids are people who are just dismissing all of animation, or choosing to be ignorant.
My advice is to try and educate people instead of getting mad. Try to show them where the truth is. If they still feel the same way, who cares. You tried to show em. Just means more fandom for you!