The late 80s and 90s were outstanding times for the Spidey books. I was 15 when I read ASM 300, and I was at a point where I was already bored with teenage heroes with high school as a backdrop and villains who wanted to take over the city/world/galaxy. When I saw Peter facing marital troubles, worrying about Mary Jane's pregnancy, and facing down ferocious lunatics like Brock and Kasady, comics grew up for me. That's when I knew they would be a life-long passion, and not something left to gather dust in my old toy box.
Eddie's had plenty of different motivations over the years (he cracked me up when he was detoxing drug addicts without their permission) but his initial one was anything but simplistic. To properly convey Eddie's hatred of Spidey, Eddie has to hate his own life first. Spidey is the avatar of Eddie's failures, ones that often came with sincere effort, and his shattered relationships. Venom, at least the true Eddie Brock version, can't have an origin that is pathetically cheesy and lackadaisical.
SM3 is the character's low point, and I'm talking drunk Vanilla Ice eating week-old ramen out of a dog dish in soiled tighty-whities low. Even the Phineas and Ferb: Mission Marvel appearance was less embarrassing than the no-origin symbiote and Blowpher's vomit-inducing dialogue delivery.