Jean and Eren initially share a fierce rivalry which stems from their differing view points: while Jean sees Eren's eagerness to join the Survey Corps as suicidal and foolish, Eren sees Jean's desire of joining the Military Police as cowardly and selfish. It was actually Jean's desire to outdo Eren that would push him to improve himself during training. Despite their bitter rivalry, which would occasionally turn violent, Jean also respects Eren to a certain degree, admitting that he lacks the latter's courage. Upon realizing Eren's potential as a Titan shifter and the hope he represents for mankind, Jean sets aside his enmity for Eren.
EREN PRESPECTIVE
As Eren's main rival, his temperament is the very antithesis of Eren's. Where Eren is hotheaded, he is collected; and Jean is pessimistically pragmatic as Eren is idealistic. Jean believed anyone who wished to join the Survey Corps was a suicidal fool, while Eren regarded those who looked down on the people who wanted to fight the Titans with contempt. Initially, they were able to resolve their differences in a civil manner despite starting off on the wrong foot. However, this friendliness was short-lived, as Jean became jealous when he saw how familiar Eren was with Mikasa. A fierce rivalry soon budded between them, with the two constantly provoking each other and getting into fistfights. In addition to insulting Jean to his face, Eren also seems to be fond of saying Jean has a "horse-face" behind his back. In the wake of the Battle of Trost however, Eren and Jean seem to have set their differences aside and stopped antagonizing each other. Though they still quarrel as much as before, their animosity has noticeably lessened.
So they have a rivalry between no romantic relationship and blame Jean because due to him their arguments became violent and not Eren okay.
COMMENT!!!!
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GUYS I WILL CALL THIS GUN MIKASA. AND IF I EVER GET MARRIED WITH A GIRL IT WILL BE THIS BAD GIRL RIGHT HERE.
