They don't. Neither do the Tzimisce. In fact, both are worshipped, active leaders of both clans.
The real hate-fest starts during the inquisition, where inquisitors - real, hardcore witch hunters with Dark ages True Faith - start hunting down
everything. Elders get dragged out of their labyrinths during the day into the sun, vamps caught feeding are staked and destroyed - for the first time ever, shit gets real for the vampiric population. And the elders panic. They throw their childer as bait to the hunters and do their damned best to run away while they burn. The young vampires get pissed off and unite to form the anarch revolt, a purge of the elders of each clan. Lasombra is (supposedly - well, he lets Gratiano do it) destroyed, and the Eldest... Well, you'll see.
But the elders rally and put their almighty feet down, and the revolt is crushed. In the convention of thorns, which you will attend, the Camarilla is formed to ensure another inquisition, and another revolt, never happens again.
But with the formation of the Camarilla, the Sabbat also comes to life. These are the vampires who wouldn't give up, no matter what. They became the Sword of Caine and they struck on the very night the Convention of Thorns ended, an act of defiance that ends with... Well, you'll see.
They also create the Vaulderie to allow more childer to break the blood bonds, by... Well, you'll see that too