I haven't been here very long but I've thought that expressing disagreement isn't the purpose of a downvote at all. Instead, it's meant to indicate that a post detracts from the discussion and probably shouldn't have been posted to begin with. Using downvotes to express disagreement would only result in discussions becoming more intellectually homogeneous, which would make the site much less valuable.
I'm not sure how the site can encourage people to use downvotes more appropriately, but I think that there is a higher risk of having trolls pollute the site than of downvotes deterring legitimate discussion (has anyone felt like leaving the site or not posting a comment because you feared that your perspective would get you down-modded? I'm not aware of such an instance but if it has happened to someone than that is a big problem that should be talked about).