Not every conflict occurs because a villain showed up to ruin everything. Sometimes, problems arise from well-meaning characters who can't stop sabotaging themselves. Anime characters who are their own worst enemies can be fascinating, as the true battle they fight occurs within their minds.
In some cases, the fallout from a character's self-sabotage dominates the plot. Despite the title of the series, the protagonist of No Matter How I Look at It, It's You Guys' Fault I'm Not Popular! routinely lets her anxiety get in the way of forming meaningful relationships.
Other characters fight real battles, but still have to contend with their inner misery. Throughout Neon Genesis Evangelion, Shinji Ikari begrudgingly takes down Angels, but the show's greatest conflict involves his self-perceived worthlessness. Regardless of the surface level issue, it's often characters' relatable inner strife that makes a series worth watching.
Sasuke Uchiha wants desperately to have a family, but he sabotages his desire at every turn.
For a large chunk of the series, Sasuke swears revenge on his brother Itachi, who murdered their family when Sasuke was eight. Despite his poise, Sasuke never considers why his sibling committed such an atrocity. By the time he realizes the Konoha government forced his brother's hand, he's already killed Itachi, making Sasuke the sole surviving member of the Uchiha clan.
With his brother gone, Sasuke transfers his rage onto his city's government, but his efforts are fruitless, as the man who condemned his family was part of a splinter group that no longer exists. When his rage subsides, he spends the remainder of his life buried in ninja work, and completely ignores his daughter.
Sasuke never achieves the revenge he longed for, and nothing can truly absolve his pain, as he repeatedly makes choices that run counter to his happiness.
Being a hero involves more than just superpowers; if you don't have the charisma to match, you won't get far. Katsuki Bakugo is amazingly strong, but his sour attitude makes his dream of becoming a pro hero exceedingly difficult.
Bakugo interprets kindness as condescension, and rejects people who genuinely want the best for him. He ignores his teachers' criticism and praise with equal disregard, which makes it difficult for him to learn from his mistakes.
To further complicate matters, Bakugo routinely becomes enraged in public. This tarnishes his reputation, and makes him a target for coercive villains who want to capitalize on his anger. While Bakugo's heart is in the right place, his demeanor is totally at odds with his ambition.
While the sudden appearance of Angels (or alien monsters capable of wiping out the human race) is a big deal, the greatest conflict in Neon Genesis Evangelion occurs inside the protagonists head.
Shinji Ikari's parents were never there for him. His mother died 11 years before the start of the series, and his cruelly withdrawn father focuses on work, and never acknowledges his son's feelings. This isolation takes a toll on Shinji, and by the time he's 14, he's fully disillusioned with the world.
Even when Shinji is chosen to lead the fight against the Angels by piloting an Eva, he's still convinced his life is worthless. His persistently negative self-image leads him to hesitate at crucial moments, and push away anyone who attempts to get close to him.
By the end of the series, humanity is well on its way to becoming a single conscious entity, yet the final moments of the show are devoted to Shinji's recognition of his inherent value as a person.
Raw skating talent doesn't mean much if you're too depressed to practice. After suffering a crushing defeat, Yuuri Katsuki is so distraught that he almost retires from skating. He eventually regains a feeling of self-worth, but to do so, he needs a lot of help from Victor Nikiforov, his former idol who becomes his skating coach and fiance.
Following his emotional recovery, Yuuri takes second place in the Grand Prix, which he considers a smashing success. To get back on the rink, he had to overcome his insecurities, so beating other skaters isn't that important by comparison.