As we learned in the first season, the prevailing reason Sandor hates his brother stems from a confrontation the pair had as children. Gregor's mean-spirit and oppressive nature led him to press his young brother's face to a fire after Sandor found and took pleasure in a toy his brother discarded. The punishment continued until the family's servants intervened, but the right side of Sandor's face sustained severe burns that scar him physically and emotionally — that's why the Hound showed an intense fear of fire during the Battle for Winterfell. In addition, the books suggest that Sandor believes his brother murdered his sister and father, whose death remains a mysterious hunting accident.
On the show, the brothers grew up to work together in the Kingsguard, where Sandor grew increasingly disgusted by his older brother's bloodlust. This friction came to a head during a jousting tournament to celebrate Eddard Stark's appointment as Hand to the King. Gregor lost a round to Loras Tyrell and chopped the head off his own horse in frustration. He then proceeded to knock Loras off his mount and strike the man down with his sword until Sandor interveneed. The brothers engaged in a bitter battle that only ended when King Robert Baratheon demanded they put down their weapons.
Sandor left King's Landing in the second season before the brothers could resolve their life-long feud, but they had a brief reunion at the wight demonstration in the dragon pits during the seventh season finale. The scene crackled with tension, but with the visit being one of truce-making nature, the Hound restrained himself. Instead, he took a verbal stab at his older sibling, saying, "Remember me? Yeah, you do. You're even fuckin' uglier than I am now. What did they do to you? Doesn't matter. That's not how it ends for you, brother. You know who's coming for you. You've always known."
Tough words coming from the smaller of the pair. Yet, when we last see Sandor in season eight, he's making good on his word by traveling along the road to King's Landing with Ayra Stark, who's just about the best fighting partner in Westeros.
