Why is applefur jealous of marshwing ?

Her jealousy definitely didn't start off murderously strong. It was pretty standard stuff before the Dark Forest twisted it into open hate.

Marshwing and Applefur are from the same litter, but Marshwing's life is charmed. He's saved from an eagle, by the warrior who becomes deputy of ThunderClan, surviving serious wounds. He's a marvelous apprentice. He grows quickly into a respected warrior. He's picked to go on the journey to save the lake at the beginning of OotS.

Basically; He's a great warrior. It's not too out of left field to be jealous of him.

Another dimension I do want to add though-- Toadkit died in the fox trap that canonically kills Marshkit. He might have died saving his brother. I think it could be VERY juicy if the Dark Forest starts encouraging Applefur to blame Marshwing for this, saying that he was supposed to die instead.