Pouting
The pout is a beloved anime expression. A character's misfortune is the best sign of mild annoyance, playful frustration, or a desperate cry for attention. This is typical of a tsundere who will not admit they care or a younger sibling who said no. Pouting is not as dangerous as anger or sadness. This funny illustration shows that the character is upset but just needs a head pat.
Artists work hard to make this expression cute. The character's puffed cheeks, which resemble an angry squirrel hiding acorns, are most important. This usually goes with a stubborn look, a small downward curve of the mouth, and tightly crossed arms to block out the world. They may also have a small comic anger mark on their forehead or a "hmph" text bubble above their head. Instead of strong shadows or serious lighting, this character art uses exaggerated body language to express itself.
Pouting characters are adorable because they are just right between angry and cute. A quiet, childish tantrum by a stoic hero or fiery main character is charming. It humanizes them and makes the show more fun. Having a cute but angry waifu or husbando as your wallpaper is odd but fun.