There was a plan to put a Dislike button on posts in Facebook but it did not push through with the implementation for unknown reasons although one newspaper columnist said that Facebook avoided adding a negative flavor to the site. A dislike button may cause a flame war among friends so maybe that's the rationale. But for me, I would love to have a Dislike button to show my Facebook friends that I don't like their nonsensical posts.
Leaving out a dislike button only makes the absence of you clicking the like button as an assumed dislike of the post especially if you know the person who made the post well because the question of why didn't you click like on this or that post will eventually come up at some point and then comes the revelation you dislike it and thus starts the argument.
If a flame war can erupt between friends over a dislike on Facebook then you don't have friends at least not amid that group. I don't know what you have with that group of people but friends is not it.