Actually, I think it could be argued that animals do, by instinct, fear death. When life is about survival, death becomes an enemy. Thus, when approached with impending doom, an animal will cower in many cases.
Besides that, I’d rather not take my life lessons from and emulate a less intelligent being.
Aside from that, it is true that we should not fear death, and I’m sure some do not. But in reality, most of us do. The unknowable, unsearchable, abrupt ending to what we call life just seems to haunt the vast majority of humans.