well it doesn't seem so bad.
besides if he hated parker so much, why doesn't just storm his house and shoot him?
Personally, i don't see the need of highlighting a hate for a human being. it would be much more appropriate for the hatred to be towards spiderman in this case.
For me venom knowing that spider-man is actually peter parker is much more important than finding out that peter parker is actually spider-man. I know it sounds crazy but finding out the alter ego of a hero is much more of an advantage than going after a civilian and finding out what you thought was an easy task actually ended up with you getting your ass kicked by spider-man.
you're right we don't know anything but that line does imply alot towards venom's actual motivation when it does come along eventually. it's quite clear his angst is against pete and not spidey AT the present time. It just makes me wonder if stealing someone's girlfriend is enough to justify such a reaction, especially when we saw it happen in the first film and harry was pretty decent about it all.