The clause was added after forum #189171 and topic #18829, where paws was aliased to animal_hands. I must have missed that BUR, because the unfortunate result of its approval was a decent chunk of animal_feet posts (which were only tagged paws at the time) suddenly being tagged animal_hands, and without much of a method to search for these mistags. But that's a different discussion.
As for if the clause should be removed, it seems rather short-sighted for the reasons Trouble Windows has pointed out. Not all furries even have animal hands, and users who weren't aware of the clause (myself included) have naturally continued to use the tag, pointing to the clause's unintuitiveness. As such, I'm in firm support of its removal from the wiki.
Trouble_Windows said:
Also should probably be figured out if pawpads on humanoid hands by themselves warrant this tag. That's not really a major thing though, just a personal annoyance. My main issue is the furry exclusion.
The phrase "animal hands" shouldn't be taken too literally here. If I'm searching for animal_hands, then I'm looking for "animal-like hands", not just "hands that are 100% identical to a real animal's hands". To put it bluntly, the notion that posts like post #5747083 should be excluded from an animal_hands search is absurd.