For what it's worth, I still cast my vote to use those buttons, but can't think of any *new* arguments to move the conversation forward.
The ... biggest counter-argument is that because we are an anonymous forum for newbies (we don't conduct background checks), a determined angry author could artificially raise the number of likes in a discussion, people might mistakenly consider a highly-voted post to be 'authoritative' about the discussion, next thing you know, we have a shit-storm on our hands.
Something you need to keep in mind, is that as far as fanfiction goes, we want a story to be able to stand on it's own - it should not become a favourite just because of a number next to it (as Shirotsume indirectly pointed out).
With that in mind, I (sadly) can't think of a good reason to push for actually making use of those 'like/unlike' buttons. Nearest I can think of is spacebattles where they have a similar system (that I admire). But "the other guy is doing it, so we should too" is a really, REALLY bad justification for doing anything. Besides, they (allegedly) have better funding and IT support than us.
-chronodekar