He's a perfect Spider-Man villain for a few reasons.
Peter started his crusade after Ben's death. That tragic event compelled him to save as many people as possible. This is compounded by the loss of Gwen not long into his career. Parker is driven by an almost desperate need to protect life. Carnage then, is his biggest nightmare.
Most of Spidey's rogues want to either make money, or take over a territory or desire power; everyone from the Goblin, to Ock to the Kingpin are all fixated on lofty goals and whilst they'll all kill, that's just a means to an end. Other's have a personal grudge against Spider-Man, like Venom or Kraven. These are villains who are simply a direct threat to Peter and not his loved ones or civilians.
Carnage is something different, he the the physical embodiment of murder. He kills for pleasure. He kills for the fame and celebrity it brings. He kills at random and in large numbers. His look is a walking, blooded body. There's no plan, no grand scheme. Carnage just likes killing and the infamy it gives him. He is the polar opposite of Spider-Man. One wants indiscriminate preservation of life, the other craves for the indiscriminate termination of life.
There's another facet to Carnage's character though; the fact that Spider-Man can not stop him. Every other villain and challenge he's faced, he's won the day alone at some point. No matter who challenges the Spider, Parker has put them down. Peter has never defeated Carnage all by himself. He's needed Venom and the Fantastic Four, or Iron Man, or the Avengers, or most of New York. The closest Peter has come to besting Carnage, was when Cletus was tricked into trying to kill his one and only childhood friend without the aid of the symbiote, and Peter sucker punched him from behind with a giant piece of lumber. Every other time they've faced off, it's taken a small army to bring him down. Carnage isn't just a walking obituary, he's one that Peter is powerless to stop.