I can't think of any examples
irrational behaviour from the animal kingdom offhand, which comes as
a bit of surprise. Even seemingly stupid suicidal behaviours like
standing on hind legs and squeaking when a predator is spotted turn
out to have rational explanations from the selfish gene's perspective.
Irrational behavior shows up, both in the animal kingdom and in human
culture, where scenarios exist that there hasn't yet been time for
genetic evolution to adapt to. For instance, a deer freezing in the
headlights of a car is irrational because the deer could instead run to
safety. An employee freezing in fear instead of asking the boss for a
raise is the same kind of thing. Our irrationality stems from the fact
that our modern culture is so far removed from the world we adapted to
genetically in prehistoric times.