It is pretty sad when the value of something is determined solely by how "beautiful" it is: If a person is ugly, s/he has no value. If a building is ugly, tear it down. If an animal is ugly then let it go extinct.
This kind of thinking makes me sick to my stomach and embarrassed to be a human being. There are plenty of things that might not fit someone's definition of "beauty" that serve a great purpose.
No matter which side you are on regarding the "god" issue, there is no reason for any animal to be allowed to go extinct.
If you believe in "god," then you are bad-mouthing a creature created by him/her -- and who are you?
If you do not believe, then you understand that animals have evolved to fit into a certain cycle in nature, and any animal removed from the cycle will damage the entire cycle. Either way, no animal should be allowed to go extinct.
I certainly hope the writer at Slate magazine who wrote this little piece was trying to make fun of people who call the aye-aye (pictured) ugly and want it to go extinct -- and not advocating it himself.
[Thanks to Matt for this tip.]