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Eren is very determined. He is also very impulsive, not always thinking before he acts. He is shown to be very brave, sacrificing himself to save Armin.
Eren is best described as hardheaded, strong-willed, passionate, and impulsive, which are attributes of his strong determination to protect mankind and eventually escape the Walls. As a young child, he was so intent on joining the Scout Regiment that he argued with and shouted at his mother, referring to the people in the village as "silly" and compared them to complacent livestock.
As a child, Eren cared deeply for Armin, his best and only friend before he met his adoptive sister, Mikasa, and most importantly, his family, risking harm and even death in order to help them. This quality was most often demonstrated in the form of Eren taking on the larger boys who would bully Armin without hesitation; more tragically when he desperately attempted to lift the rubble crushing his mother during the Titans' assault in Shiganshina. In contrast, Eren is also capable of displaying very violent behavior in the defense of people he does not even know. This is highlighted when he brutally slaughtered two of the human traffickers who captured Mikasa in order to rescue her, despite the fact that they were total strangers at the time. Since witnessing his mother's gruesome demise and losing contact with his father, his fierce protectiveness to those he has left has only intensified.
Eren has a number of defining traits that date back to his childhood. He came to share Armin's awe of the lands beyond the Walls after the latter showed him a book depicting the wonders of the outside world, and decided to see it all for himself. This led him to develop a scornful attitude to anyone content to live and die within the confines of the Walls without ever setting foot outside. This very contempt may have been the reason he did not easily make friends with his peers. He resented both the Walls that "caged" them in like cattle and the Titans that had driven humanity to erect them in the first place. As a result of this, he greatly admired the soldiers of the Scout Regiment, regarding them as "heroes," and wishing to join their ranks as soon as he became eligible for enrollment. He easily took offense when anyone spoke badly of the Scout Regiment, and his determination to join their ranks caused friction between himself and his mother, as well as to Mikasa.
Eren had a marked lack of self-restraint that often led him into trouble, causing both his friends and family to worry about him. His limited self-control extended to his temper, and as a result, it was short at best and murderous at the very worst. When sufficiently provoked, his anger could drive him into a frenzy, accompanied by horrific levels of violence. Like many children, he tended to view the world in terms of black-and-white, having great compassion for humanity and its plight, but deeming those individuals who deny others their freedom as worthless scum unfit to be left alive. He also had the habit of thinking with his heart rather than his head, even in situations where his own life was in danger.