It's not that they aren't rational per se. Rather all mammals have social dominance preprogrammed into them.

These guys will, as you've noticed, loudly demand you to go away . . . while they approach you and then aggressively follow you around as you try to keep away from them . . . worse if they are presently in a group. The behavior of whether they follow you or not and continue to attempt to threaten you or not depends on where they see you in their dominance hierarchy.

I suggest it's not so much that human brains cannot distinguish threats to body from threat to egos — which is somewhat true.

The less intelligent they are they less their brain can tell the difference between an intellectual argument and a physical argument — and this in the context of position in a hierarchy of social dominance. Because when humans evolved there was no such distinction. (I refer you to this book: Satoshi KANAZAWA, The intelligence paradox, Hoboken: Wiley, 2011)

We live in an age where, despite everything, persons survive far more independently than ever before. In the past, when there was no significant production of anything, social group and therefore social dominance hierarchy, was survival.

Generally you might be interested in these two classic papers on the subject: (1) Eugene BRODY, Enger ROSVOLD, Influence of prefrontal lobotomy on social interaction in a monkey group, Psychosomatic Medicine, 14(5):406-415, 1952(9)., (2) E. ROSVOLD, A. MIRSKY, K. PRIBRAM, Influence of amygdalectomy on social behavior in monkeys, Journal of comparative and physiological psychology, 47(3):173–178..

(I might write a post on this subject.)