Most despised Chargers: Eli Manning
To be fair, Eli Manning never actually played a snap with the Chargers as his career with the franchise lasted a very short amount of time. The Chargers selected Manning with the first overall pick in the 2004 NFL Draft only for him to demand his way out, eventually leading to the trade that netted Philip Rivers.
In hindsight, this was probably the best-case scenario for the Chargers. Rivers was the more talented quarterback and the Chargers got additional assets in the deal. Giants fans will point out that Rivers has no championships and while Manning made some heroic throws in his two Super Bowls, he was also carried by an elite defense in both years.
Put Rivers on those Giants teams and they would have won two Super Bowls and then some. Put Manning on the Chargers and his career likely goes far worse than Rivers' career did with the Bolts.
Getting the best quarterback in franchise history out of this definitely helped soften the blow and there are not any Chargers fans out there that wish Manning would have just stayed with the team. But his blatant disrespect for the organization and the fanbase still makes him despised.