I can understand that some people might need a day off to cope with the loss of their pet. Really.
And saying that doesn't make the loss of a pet the same as the loss of a child, that is just pants on head retarded. Some people need a year or more to cope with the loss of a child. A day for a pet--doesn't seem too outrageous.
Oh, and when I say "need", I mean, they get some sort of satisfaction/closure out of spending a day in reflection or whatever. Plainly it is a want, not a need. But I respect people's wants, if they are good reliable people.