An unsympathetic villain
Penguin is far from the first HBO series about an American-Italian gangster with mommy issues. Naturally, from the first episode, viewers began comparing Oz to another iconic TV mob boss, Tony Soprano. And for good reason, since their lines rhyme for much of the first season. However, the two characters differ from each other in one key way: Oz remains a villain from the beginning to the end of the show, showing no sympathy for anyone but himself.
While most villain shows try to either tell the story of a character's transformation into a killer or humanize the protagonist over the course of a season, Penguin takes a completely different path. The creators initially declare that there is nothing bright in Oz. Then they repeatedly give the audience a false trail: they show Farrell's character helping Vic, taking care of his mother, or giving a fiery speech to the poor.
However, in all these moments, Penguin is driven not by the desire to achieve justice or take revenge for something, but by the banal need to survive and move up the food chain. Therefore, when someone from Oz's entourage becomes unnecessary to him, the character is ready to get rid of him in that very second.
The important thing is that Oz sticks to his original plan. But audiences, schooled in stories of villains with hearts of gold, continue to believe Penguin's tales of both his troubled childhood and his plans to change Gotham for the better. By the end of the series, when the creators show Oz's biconcave form for the last time, the audience has no sympathy for the character. This creates a villain that is both repulsive and a series that is compelling to viewers.