The Starks vs. Lannisters are one of the central quarrels in Game of Thrones. Ned Stark, the Lord of Winterfell and Warden of the North, often finds himself at odds with Ser Jaime Lannister in the first season of the series. While it may seem like this feud starts with Jaime's heartless act of pushing Bran Stark out of a tower, the animosity actually began years before the pilot episode.
Source：https://www.cbr.com/game-of-thrones-why-ned-stark-hates-jaime-lannister/
