10 Worst Things Venom Has Done To Spider-Man
2. Tormented His Loved Ones For The Fun Of It
One of the very first things Eddie Brock did after obtaining the Venom symbiote was pay a creepy visit to Spider-Man's wife, Mary Jane Watson-Parker. He did this for absolutely no reason other than to scare the absolute Hell out of her and get under Spidey's skin. In addition, he would frequently to the same to Peter's beloved Aunt May.
He had nothing to gain from these encounters and had no plan going in. He simply did it because he knew the pain it would cause for everyone involved. It's one thing to use your rival's loved ones as a poker chip to get what you want (which Venom also did, by the way), but it takes a special kind of sadist to do it just because you feel like causing fear and anger for the sake of fear and anger.
In addition, keep in mind that Venom knows every single thing Spider-Man knew up until he ditched the alien costume. This means that he knew all about Gwen Stacy's death at the hands of the Green Goblin and decided that the best way to cause Spidey unbearable distress was to insinuate that another person he dearly loves would be next on the proverbial chopping block.