It's annoying because Zelena's character doesn't have to be written or acted out this way. She has legitimate grievances against people like Regina, meaning she can be taken seriously when she brings them up like a normal human being. She doesn't have to snarl. The way she whines is closer to Regina, but she has a completely different background. Growing up as the daughter of an abusive woodsman wouldn't make her an entitled heiress who feels everything belongs to her. If the flashbacks in "Sisters" are any indication, she would be grateful for any kind of acceptance or recognition.
I don't think the "jealous bitch" persona, which is supposed to be pivotal to the character, fits her story. Rebecca Mader can act really well when she's directed to act like an adult. I truly think the directors and writers made a mistake when they hired her to play someone so unlikable. Zelena's got the potential to be a sympathetic character, but making her the green-with-envy Wicked Witch of the West was just dumb.