Like I said, that's one of my favorite traits about Venom and one of the things that makes him one of my favorites. Speaking of Eddie Brock, back in 2007 (before all the ANti-Veom stuff which I really enjoy), there was a story in The Sensation SPider-Man where Brock is in the hospital and he literally cuts himself thinking that he's freeing the symbiote. It's a fantastic loook into Brock's mind at the time.
It's really a look inside Borck's state of mind back before Anti-Venom.
Here's 2 random panels from the issue. These are not next to eachother in the story, just random panels as I said.