Let me begin by pointing out that looks don’t matter much. It never appears that Isayama is jealous of Jean because she is ugly. Could you take a look at him? If I may say so myself, he’s a dashing young man.
The moment Jean Kirstein met Eren Yeager, she was jealous of him. In other answers, Jean claims that he is jealous of Eren because Mikasa loves him, and while that certainly adds fuel to the fire, I believe Jean’s jealousy lies in the fact that Eren is as accurate as they come.
The first time we meet Jean, he aspires to become a police officer in the inner wall district. Instead, he picks on people and behaves like a bully in many ways. The fact that he hides behind a tough guy persona shows that he is very judgmental of everyone, including himself. Until Eren gets involved, Jean continues to rant about the survey corps.
Eren joins the squad as a tough guy with a mission, not some fake shite. In contrast to Jean, he will not pick on people or start fights, but he will still stand up to bullcrap and stand up for what is right. As a child, Eren killed a man without hesitation, so he didn’t need to justify himself like Jean.
Whenever Eren says or does something, he means it, which makes Jean jealous of him. Even though Eren is literally in the belly of the beast, he continues to vow to kill them all and ends up doing so.
Along with Armin Arlert, Mikasa Ackerman is one of the series’ deuteragonists.
Eren Yeager rescued Mikasa after human traffickers murdered her parents, and the two of them lived with his parents, Grisha and Carla before Wall Maria fell. In Hizuru, she holds considerable political power and is the last descendant of the Shogun clan that stayed on Paradis Island.
Despite her desire for a peaceful life, the 104th Training Corps considers Mikasa, the best soldier among its soldiers. As one of the Survey Corps’ most valuable assets, she enlists to follow Eren and protect him. As a member of the Corps, she is currently serving as an officer.
Eren has a persuasive personality. Throughout the Trost arc, he gives persuasive speeches about the value of fighting the titans. Eren’s speeches, in Jean’s view, are dangerous. They aren’t disingenuous like the government’s rebranding of the cull as an “Operation to Retake Wall Maria” but are careless. Having friends who love him is already a nice thing for Eren. Throughout the manga, Jean doesn’t seem to have any friends (he doesn’t seem to be able to ingratiate himself well with others). I guess he needs to be self-sufficient, but he wishes to have companions like Mikasa and Armin, who would take good care of him as Eren does. He doesn’t want to become like Eren, someone charismatic but so focused on a goal that he doesn’t always appreciate the people around him. (This is Jean’s reading of the situation, not necessarily an accurate representation of Eren’s relationship with Mikasa and Armin, who have their reasons for acting the way they do, as well; Jean’s reasoning seems a bit presumptuous, but the nuances it a bit later in the series, as he continues to remind Eren of his obligations to his friends and allies).
To summarize, Jean envies Eren’s relationship with Mikasa. Still, it’s a symptom of Jean’s more excellent outlook on life: Value your life.
Please don’t throw it away carelessly. Be responsible to those who count on you and support you.