Wikipedia post the photo on Wikimedia Commons. The name of this part of Wikipedia suggests the photo is in the public domain.
Naturally, like many self-respecting photographers, David wants the photo taken off. Perplexing problem if you ask me, because the photographer wants credit for a photo he clearly didn’t take (yes, the monkey took his selfie), and Wikipedia is being equally unfair to the photographer (the closest human to the point of origin of the photo) to use legalese to keep the photo up; disrespecting the ownership of the photo.
The conflict is in a gray area because the law of the land on copyright varies around the globe. So, if the laws of the land(s) were applied to such a case, then the photo could stay on Wikimedia in some countries, and in others it would have to be taken down, to be consistent with the laws of various countries. That would mean Wikimedia would have different content for different countries… and this is where the Internet might be heading. I think content creators everywhere don’t want this to happen, because we would like to think you could find any site anywhere in the world and have all of the content wherever we might be.
If David tells me to take the photo down from my site, I will oblige him. No reason to fuss over one monkey selfie. There will someday be hundreds of other monkey selfies, no doubt.