Why is Levi Akerman from Attack on Ttian popular?

Many people say that Levi Akerman is their favorite anime character.

There can be many reasons:

First of all, he is not childish. He looks mature. Main characters like Erwin and Hange are childish and sometimes behave like nuts. Erwin's masculine and calm voices can be contrasted with Eren's high pitch, high volume voice.

Second, he is a tragic character. Girls love male characters with tragic or traumatic childhood. Motherly instincts are instantly aroused with this character.  Levi's mother was a prostitute and died from an unspecified disease leaving him an orphan. He was then raised and subsequently abused by his psychotic uncle, Kenny.

Third, he has a unique charisma. He doesn't respect authoritative figures and call some important people "pigs" at Eren's trial.

Fourth, He is loyal. He follows Erwin's orders regardless of the results. He actually cares about his team members and he can sacrifice himself to the extent of injuring himself. He exhibits very little emotion but feels things very deeply inside.

Fifth, he is a great strategist. He think five steps ahead, measuring strengths & weakness of each situation, and adapting his actions accordingly. He is a sharp thinker. These characteristics make him stand out from Kenny's squad. He also understands when to back down, often for the sake of others.

Sixth, despite the fact he is petite, he is good-looking and perfectly formed.

That being said, Levi is not perfect. He has issues with the Obsessive Compulsive Disorder. He doesn't like being touched and he's obsessed with being clean. It is also assumed that he is suffering from PTSD, as he can sleep for only short time. He had traumatic experiences as a child so he uses violence to get his own way. In a way, he is too rough. He also made some of the worst decisions, such as leaving Farlan and Isabel alone, so that he could go and kill Erwin.

Conclusion:

Despite Levi's personal weaknesses, he is an attractive character.