Necessity

"Grisha... today, your son became a soldier."

- The instructor observes Eren's progress

Hitsuyō (必要) is the 3rd chapter of the 4th volume and the 16th chapter overall of the Attack on Titan manga, written and illustrated by Hajime Isayama.

Overview
Still having trouble with his vertical maneuvering equipment training, Eren tries the test on his own with Mikasa and Armin, but quickly fails. Becoming anxious at the ridicule from his peers and Mikasa's diminishing faith in his abilities, he asks Jean and Connie for advice, only to receive more ridicule. He then turns to Reiner and Bertolt, who tell Eren and Armin the story of their town being attacked by Titans two years before. Having bonded with Eren and Armin, and impressed with Eren's intense willpower, Reiner gives him some advice and motivation.

When the time comes for Eren's official retry, he successfully balances for a while before losing his balance and falling. He begs the instructor for another chance, and the instructor orders Thomas to switch belts with Eren. After the switch, Eren can balance perfectly. The instructor explains that Eren's belt had been broken somehow, and that he has passed the test. As Eren rejoices, the instructor thinks to himself that Grisha's son has become a soldier.

Summary
Eren is still having trouble balancing in his training for vertical maneuvering equipment and tries to get tips from Mikasa and Armin. However, it does not go well and he hits his head on the ground knocking himself out. After some remarks from other trainees, they go to the mess hall to eat while Eren recuperates. Mikasa says that Eren may not be cut out for being a soldier and suggests that he could get another job. This angers him and he reminds her of what happened when the Colossus Titan attacked. Angry, Eren leaves the table. Mikasa tells him that if he were to quit, she would follow. However, by the time she is done talking only she and Sasha remain in the mess hall. Sasha asks is she can have Mikasa's unfinished bread. Taking the bread, Mikasa eats it in front of her.

Back at the barracks, Eren is asking people for advice. After a few dead ends with Jean and Connie, he is pointed to Reiner and Bertolt. While they do not offer any advice at first, knowing where Eren and Armin are from, they ask their reason for joining the military as they know what Titans can do. They both say that they could not just sit around and do nothing. Bertolt tell them where they are from and how they got here. After the Colossus Titan attacked the Wall, the Titans got to their village before the warning did. They barely managed to get to their horses in time to make it to safety. He notices that Armin and Eren are not like the others, who for the most part joined out of ignorance and because of expectations. Bertolt says that he joined the military for the chance to join the Military Police Brigade, otherwise he might quit altogether. Eren comforts him, adding that after what happened to him, no one could blame him for wanting that. Eren admits his fear as well, but says that the hate he has for them is greater than his fear. After swapping stories, Reiner tells Eren to check his belt and to make sure it is adjusted and that tomorrow it should work out.

The next morning, Eren is starting his test. The instructor tells him that this is the absolute lowest requirement of a soldier and if he can not do it he can not be a soldier. He tries it again, initially keeping his balance but falling over after a few seconds. The instructor then tells Thomas to exchange equipment with Eren. With the new belt, Eren keeps his balance perfectly. The instructor sees that his belt was damaged. Eren, with a triumphant look on his face looks at Mikasa. She comes to the sad realization that he is glad that he will not have to depend on her, but claims the opposite to the others. The instructor is impressed that Eren was able to keep his balance, even if for a short time with the damaged equipment, and thinks to himself that Grisha's son became a soldier that day.

8. Vertical Maneuvering Equipment Training
''Humans move in two dimensions, so vertical maneuvering equipment training, in which they must adapt to three dimensions, is extremely demanding. Physical strength is most important, especially leg strength, though the ability to adapt to G forces (which women particularly excel at) and a grasp of three-dimensional space are also vital. When in midair, one must quickly assess the situation and surroundings, while uncommon willpower is required to keep from panicking. The various training activities include bungee jumping and gymnastics with equipment. At one point, the instructor will deliberately cut the lifeline (an "ambush" in trainee vernacular). At any rate, it would be hard to call this training "safe," but anyone who would die during this period would not stand a chance in battle against a Titan, and soldiers who manage to get through it come out with a stronger fighting spirit and self-confidence.''

Trivia

 * In the Chapter 71, Bystander, it is revealed that Keith Shadis, the instructor, broke Eren's belt so that he could not join the Survey Corps and keep his mother's wish.