This is a fallacious assumption, Homo sapiens have very large cerebral hemispheres, "lower" mammals do not, birds none at all. A hit to the cerebral hemispheres alone will not kill a human, there are many, many documented cases of people shot in the head who survived. The goal is not to hit "the brain" per se, the goal is to hit a vital part of the brain, i.e. the brain stem. The brain stem (medulla oblongata, pons, midbrain) controls autonomic functions, equilibrium, coordination, and basic sensory functions. So, you need to impact the brainstem. Having witnessed the killing of millions (literally) of animals, the way you do that is to draw an X from each ear to the opposite eye, and shoot where the lines cross. The animal will collapse on the spot.
I think witnessing all those animals being killed has been at the cost of understanding anatomy. Even in a "lower" mammal such as the primitive armadillo and in bird that you claim have none, the cerebral hemispheres are pronounced. A quick Google search reveals many article dedicated to avian cerebral hemispheres. Heck, even in the alligator which is evolutionarily lower than birds, the cerebral hemispheres are quite pronounced, though the overall size of the brain is small. Even frogs have them.
Your directions for locating the brain stem externally for shot placement suffers the exact same problem that people spout when claiming shot placement is everything. Without penetration and trajectory, shot placement is just an external spot. You can shoot animals on your X all day long and not hit the brain stem without the correct trajectory and sufficient penetration to reach it. Put another way, you have provided 2D directions to find a 3D target via another location.