Of course people shouldn't leave their animals....but... speaking from someone who's ridden out several hurricanes or their aftermath...the biggest problem is public shelters do not allow you to take your pets. The shelters opened by our city....are in schools or other public buildings and you can not take ANY animal.
It's a liability issue...
My recourse is, of course, to evacuate to someone's home inland or a motel room...but obviously many many people who don't have those options.