Unfortunately, it would be a method for people to show discontent towards another without risking any form of punishment.
For example, to show you dislike someones idea now you have to actually say it, but as to not get your post deleted or receive a ban, you need to pretty much be nice and or constructive.
Which is a good thing. The moderators do a decent job deleting nasty comments and I am glad they ultimately force people to remain civil (I bet they hate Mondays).
Disliking can be used to harass. eg. 'X player is known to make a lot of posts about X topic and Y players get 'tired of them talking' so down vote every single thing they say'

While I do feel it could be good for down voting suggestions that a lot of people dislike, ultimately it would not benefit the forums at all.