The main thing is that you can't expect everyone to like everything. If you live in a world where only positivity was allowed, everything would suck. The bottom line is that people might not like something for a variety of subjective reasons and that is perfectly OK.
Our system is built to offer a crowd-based curation process. Without the ability to downvote something you don't like, we aren't able to do such a good job of calculating the correct 'score' for that video.
What is important to realize is that the algorithm behind the scenes takes this into account. Couple of downvotes won't kill a video at all, its compensated for in the bigger scheme of things.
People always blame the internet for 'hate' but the truth of the matter is that its humans in general that have differing opinions, and when you get to hear those different opinions it can hurt. Its very hard to look past one downvote that hurts to see 99 upvotes that make up the rest.
The reason that a great deal of facebook is filled with crazy stupid garbage in my mind is their lack of a downvote button. Stuff only gets liked, and not held down by those who might catch nuances to what is wrong.
"Wu-Tang is for the Children."
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