No, I don't support this idea.

To the people saying it won't be abused, just take a look at Reddit and WoW.
The Downvote button in Reddit is supposed to be for posts that are off-topic or don't contribute to the discussion but since it enables people to hide posts they disagree with, it gets abused. Despite numerous reminders that it is not a dislike button, a lot of well-constructed but controversial arguments get hidden along with any replies.
In WoW the downvote button is for expressing dislike but again, it's abused and people use it to shut down debate.
Lovely as our FFXIV community is, we're still human and I'm fairly sure downvote button would be abused here in a similar fashion if one was introduced.

Your idea isn't getting a lot of support OP, yet it's still on the front page and people are debating it. That's how a forum ought to work. If people had the option to downvote, your thread might have been hidden and we would not be having this debate.