Doesn't sound like the most pedestrian sort of normal behaviour, does it? Myself, I find it eminently reasonable. After all, why not?
The poet Gérard de Nerval was notorious for having walked his pet lobster on a leash in the gardens of the Palais Royal, and he provided an excellent justification for it, too:
"Why should a lobster be any more ridiculous than a dog....or any other animal that one chooses to take for a walk? I have a liking for lobsters. They are peaceful, serious creatures. They know the secrets of the sea, they don't bark, and they don't gnaw upon one's monadic privacy like dogs do. And Goethe had an aversion to dogs, and he wasn't mad."
-quoted in T. Gautier: "Portraits et Souvenirs Littéraires" (1875),
translated by Richard Holmes in T. Gautier: "My Phantoms" (1976), p. 149
Of course, all the uproar over this eccentricity was in the 19th century. Had de Nerval lived in today's world, he would have found it much more tolerant of this sort of erratic behaviour. Though the subject of walking exotic pets on a leash can still be the subject of jokes (a quick search of Google, for instance, shows dozens of sites telling the old joke about "A man walks into a bar, with a huge alligator on a leash" - a different kind of blonde joke), there are also plenty of exotic pet owners out there who take the matter quite seriously.