Skin

Skin covers flesh of animals and humans
The former covered with fur and latter on the head has hair
Skin could be reminiscent of Harry Truman
Animals covered with fur, humans generally bare

Skin!
Skin!
Skin covers up animals and humans
Oh, Skin!
Skin!
Skin covers up animals and humans
Normally animals' skin is thick
But humans' is comparatively thin
A tear in skin can make animals and humans sick
Normally all hilarious and seldom sin
Skin!
Skin!
Skin covers up animals and humans
(repeat)